Originally Published: 22 MAY 22 15:48 ET

By Rachel Janfaza, CNN

(CNN) -- Six weeks postpartum, Rochelle Garza was on the frontlines of an abortion rights rally in Dallas.

"I will be damned if my daughter grows up in a state where she cannot control her own body," the Democratic candidate for Texas attorney general said into a megaphone.

Abortion rights had already been top of mind for Texas Democrats during the state's March 1 primary elections, as Democratic candidates and political operatives pointed to the Lone Star State's controversial six-week abortion ban as a warning sign for what life could look like in a post-Roe America.

But, two months later, the issue became much more pressing: a Supreme Court draft majority opinion that would overturn the landmark Roe v. Wade decision had been leaked.

"I know that everyone is angry. We should be angry because this is an attack on our health care. Because abortion is health care. Reproductive freedom is a human right," Garza said on May 3.

In the weeks since then, abortion rights has become even more central to two key Texas runoff primaries. Voting will end in those races on Tuesday.

In the runoff for the Democratic nomination for state attorney general, Garza, a civil rights attorney who previously won a case granting a detained 17-year-old immigrant the right to an abortion, is facing off against former Galveston mayor and trial attorney Joe Jaworski, who is also pro-abortion rights but lacks the same backing of abortion rights groups that Garza has.

"Women and all people who care about equal rights, even if they're not women, should be angry, alarmed and motivated," Jaworski said in an interview with CNN Friday. "Reproductive choice, at least protected by the federal constitution, is over, and this ought to be a wake-up call, a motivating call for voters, whether you're a woman or not."

The issue has also come to the forefront of the blockbuster Democratic primary runoff for Texas's 28th Congressional District, where Jessica Cisneros, a 28-year-old immigration attorney, is facing Rep. Henry Cuellar. Cuellar, a political institution in South Texas, is the last remaining anti-abortion rights House Democrat and was the only member of his party in the lower chamber last fall to vote against the Women's Health Protection Act, which would codify abortion rights even if the Supreme Court reverses Roe v. Wade.

Jamarr Brown, co-executive director of the Texas Democratic Party, told CNN that after the leak of the Supreme Court draft opinion, the party will be "following the primary runoff results to see if there are any indicators of this issue moving the electorate."

"This issue is a reminder of what is at stake in this election -- that we must fight extremism by Republicans in Texas and across the country when they attack our fundamental freedoms," Brown said.

Cisneros prioritizes abortion in South Texas

Days after the Supreme Court draft decision was leaked, Cisneros posted a video on Twitter asking Democratic leadership to retract their support for Cuellar.

"At every turn, my congressman has stood in opposition to the Democratic Party agenda. From being anti-union to being anti-choice and with the House majority on the line, Cuellar could very much be the deciding vote on the future of reproductive rights in this country and we just cannot afford that risk," she said.

Asked during a press conference earlier this month about her support for Cuellar, House Speaker Nancy Pelosi doubled down on her backing of the incumbent congressman, saying that while Cuellar is an abortion rights opponent, the Democratic Party was able to pass the Women's Health Protection Act without his vote.

"I'm supporting Henry Cuellar. He's a valued member of our caucus," Pelosi said at a May 12 press conference, adding later, "He is not pro choice, but we didn't need him."

Cuellar is also backed by House Majority Whip Jim Clyburn, the No. 3 Democrat in the House, who stumped for Cuellar in San Antonio, Texas, the same day Cisneros released her statement asking for party leadership to reconsider their stance.

For months, Cisneros has been talking about the differentiation between her and Cuellar when it comes to abortion rights.

"He doubled down on his anti-choice stance and said abortion wasn't health care. This is why I'm running, because our community deserves someone who will always fight tooth and nail for our health care," Cisneros previously told CNN in a statement.

Cuellar, according to the Laredo Morning Times, said in a Zoom event last year that he had backed "millions of dollars on health care for women," but that abortion was "not a health issue."

"For me," Cisneros said, "knowing how many people are being affected and have lost their right to health care, you just can't be a bystander."

"As a lifelong Catholic, I have always been pro-life. As a Catholic, I do not support abortion, however, we cannot have an outright ban. There must be exceptions in the case of rape, incest and danger to the life of the mother," Cuellar said in a statement after the draft opinion leaked.

"Additionally, my faith does not allow me to support extreme positions such as late term or partial birth abortions. My faith is clear: abortion must be rare & safe," Cuellar said.

CNN reached out to Cuellar's campaign and the Democratic Congressional Campaign Committee but did not immediately receive a response for comment.

Both Texas Democratic attorney general candidates vow to not criminalize abortion seekers or providers

Both Garza and Jaworski told CNN that if elected, they would not criminalize women for seeking an abortion or abortion providers.

"My commitment is to fighting for everyone's constitutional right and being the people's attorney and looking out for the people, and that does include making sure that we do not criminalize women or providers or anyone for making a healthy decision. I make that commitment that I am not going to criminalize anyone or force criminality for someone making a decision for themselves," Garza said in an interview Thursday.

Likewise, asked if he would criminalize people who sought an abortion or abortion providers in the state, Jaworski said, "I would not."

He added that he does not think prosecuting abortion is within the purview of the state's attorney general.

"In fact, I don't think it would be the Texas attorney general's province to initiate prosecution, even if I felt like doing it, which I don't," Jaworski said Friday, adding that he believes the decision will come down to "local decision making authority."

As an attorney in private practice, Garza -- who previously told CNN her candidacy for attorney general was in part inspired by Texas' six-week abortion ban -- fought in court against Texas Republican Attorney General Ken Paxton's efforts to insert himself in a case to help the Trump administration prevent her client, a detained 17-year-old immigrant, from accessing an abortion. Garza and the ACLU won that case.

"This is what we need in the office. Somebody who practices what they preach. I'm a civil rights lawyer," she said.

For his part, Jaworski told CNN he is uniquely positioned to serve as attorney general because of his litigation experience. But Jaworski has never previously fought for abortion in court.

"I've not had occasion to fight for reproductive choice in court, but I have had two major victories on difficult cases," Jaworski said, detailing cases regarding workers' rights and public housing in the state of Texas.

Jaworski told CNN that he believes the issue of reproductive rights in Texas must be looked at from an equal rights perspective and could come down to the equal protection clause of the Texas constitution.

He added that the fight for reproductive rights in Texas will require a sincere commitment to voting rights as well, in part due to Texans role in voting for state Supreme Court justices.

The Democratic nominee will take on the victor of the Republican primary race. Paxton, who won reelection by under 4 percentage points in 2018, is seeking a third term this year and has a primary runoff of his own against George P. Bush to get through on Tuesday. Texans haven't elected a Democrat to a statewide office since 1994.

National and local abortion rights groups weigh-in

The high-profile races have attracted the attention of national and local organizations, many of whom advocate for abortion rights.

Both Cisneros and Garza are supported by EMILY's List, the influential Democratic political committee that backs pro- abortion rights women for public office.

For its part, EMILY's List's independent expenditure arm "WOMEN VOTE!" has put out mailers, television ads and digital ads for Cisneros ahead of the runoff, Christina Reynolds, vice president of communications for EMILY's List, told CNN.

While Reynolds noted the group's concerted push for Cisneros, she highlighted the work of the organization to support Cisneros during both of the past two cycles. EMILY's List also backed Cisneros in 2020, when she challenged Cuellar for the first time.

Asked about whether or not the leaked Supreme Court draft opinion has changed the stakes of the race in Texas' 28th congressional district, "It's not a new issue here. It potentially makes it more real that this is going to happen," Reynolds told CNN, referring to the possibility of a post-Roe America.

"Both [Cisneros and Garza] talked about [abortion] beforehand, before the decision, and continue to talk about and raise with voters since the draft opinion leaked," she said.

Additionally, Cisneros is backed by Planned Parenthood Action Fund, while Garza has the support of by Planned Parenthood Texas Votes, the local wing of the national abortion rights advocacy group.

Dyana Limon-Mercado, executive director of Planned Parenthood Texas Votes emphasized that throughout the state, more Texans are talking about the need for abortion rights.

"We know a majority of Americans already believe that Roe should stay in place and abortion should continue to be legal, even among Catholic voters, Hispanic voters, women of all socioeconomic backgrounds," she said.

"Now, what I think you see, is more different types of voters talking about it. Maybe people who their number one issue maybe has been education or the economy and other stuff like that, this conversation has really started to dominate on politics up and down the ballot."

Ana Ramon, who is the interim executive director of Annie's List, a Texas-based group that backs progressive, pro-abortion rights women at the state level, told CNN that across the state, voters are emphasizing abortion rights as a top issue.

"We have definitely heard of interesting conversations at the doors. It's more on the grassroots level where people are talking to our endorsed candidates about abortion and access," Ramon said.

"Everything is at stake, people's lives are at stake. We know that women and Texas families, they are more likely to die of gynecological cancers, gynecological disease, if they don't have access to the resources and services they need," she said. "This is no longer about policies it's about people."