Originally Published: 28 JUN 22 20:10 ET

Updated: 29 JUN 22 01:41 ET

By Gregory Krieg, CNN

(CNN) -- On the same day a former aide to President Donald Trump's chief of staff testified about how Trump had wanted to join the throngs of his supporters at the US Capitol on January 6, 2021, Republicans in Colorado on Tuesday rejected three election deniers running for statewide office.

Mesa County Clerk Tina Peters, who pleaded not guilty after being indicted earlier this year on 10 counts related to voting machine tampering allegations, lost the GOP nomination to take on Democratic Secretary of State Jena Griswold in November. Pam Anderson, a former Jefferson County clerk, will win the Republican nomination, CNN projects.

In Colorado's GOP Senate primary, voters rejected state Rep. Ron Hanks, who showed up at the Capitol on January 6 and, though he has said he did not enter the building, has gone on to spread false claims and debunked theories about voter fraud. Businessman Joe O'Dea will win the nomination to face Democratic Sen. Michael Bennet, CNN projects.

And in the state's GOP governor primary, Greg Lopez, the former mayor of Parker, outside of Denver, lost to Heidi Ganahl, a member of the University of Colorado Board of Regents, CNN projects. Unlike Ganahl, who views Colorado's election results as valid, even if she's avoided questions about the national results, Lopez has said he believes Trump won the 2020 election. Ganahl will try to unseat Democratic Gov. Jared Polis this fall.

The GOP primaries in Colorado took on added significance with Tuesday's stunning revelations in Washington. Cassidy Hutchinson, an aide to Trump White House chief of staff Mark Meadows, told the House select committee that the then-President had been aware that many in the crowd before the Capitol riot were heavily armed and then, after his speech that morning, reportedly lunged at the steering wheel in his limousine after being told by the Secret Service they would not take him to the Hill.

Mississippi also provided a minor rebuke to Trump on Tuesday, with GOP Rep. Michael Guest defeating challenger Michael Cassidy, CNN projects. Guest had came under attack from his party over a vote to establish an independent commission to investigate the deadly Capitol riot, but -- after being taken to a runoff -- is now on track to win another term.

In Oklahoma, challenger Jackson Lahmeyer, an evangelical pastor, had criticized Republican Sen. James Lankford, whom CNN has projected to win renomination, over his refusal to endorse Trump's lies about the 2020 election.

The shadow of the Supreme Court's decision last week striking down Roe v. Wade also loomed over Tuesday's elections. In the Colorado Senate primary, O'Dea supported abortion rights in most circumstances, while Hanks had advocated for a total ban on the procedure.

Democrats across the country were also tracking Tuesday's turnout as they gauge whether the ruling has motivated a base that's been demoralized by the party's performance during President Joe Biden's time in office.

Republican primaries have also attracted some gamesmanship from Democratic groups, who have sought to elevate GOP candidates they believe will be less viable in general elections. In the Colorado Senate race, Democrats had tried to boost Hanks, for example. In the gubernatorial race, they were hoping that Lopez would defeat Ganahl.

It was a similar story, but with a different outcome, in Illinois, where former Aurora Mayor Richard Irvin, the first Black candidate elected to the office, was the establishment choice to square off with Democratic Gov. J.B. Pritzker. But state Sen. Darren Bailey, who had Trump's backing, will win the GOP nod, CNN projects.

Illinois primaries

Illinois was home to the largest and most competitive slate of congressional primaries.

Two of them pit incumbents who were drawn into the same seat during the state's redistricting process. Democrats chose Rep. Sean Casten over Rep. Marie Newman, CNN projects, this time to represent them in the new 6th District. Newman came under fire during the campaign over potentially damning findings from an ethics probe. (She has denied the allegations against her.) The race was expected to be tight, largely because Casten's current constituents were mostly drawn into a different district.

On the Republican side, in southern Illinois' new 15th District, Rep. Mary Miller is projected to have defeated fellow incumbent Rep. Rodney Davis, who was considered the more moderate choice of the two. Miller, a freshman, is a Trumpist flamethrower who, in a speech alongside the former President over the weekend, declared the Supreme Court's Roe ruling a "victory for White life." (A spokesman claimed she had misspoken and meant to say, "right to life.")

Three more Democratic primaries, two of them for open seats and another featuring a challenge to a longtime incumbent, also competed for headlines. In Chicago's 7th Congressional District, Rep. Danny Davis will defeat challenger Kina Collins, a gun violence prevention activist, CNN projects. Collins, who lost badly in a 2020 challenge to Davis, had the support of progressive groups led by Justice Democrats -- and the fundraising might that comes with it -- this time around, but it wasn't enough.

Progressives succeeded in their efforts to gain influence in the Democratic House caucus by winning the nomination for the open seat in Illinois' 3rd District, which includes areas previously represented by Reps. Chuy García, Raja Krishnamoorthi and Casten.

CNN projects that state Rep. Delia Ramirez, who was endorsed by García, New York Rep. Alexandria Ocasio-Cortez, Vermont Sen. Bernie Sanders and Massachusetts Sen. Elizabeth Warren, will win a four-way race.

The campaign arms of the Working Families Party, Congressional Progressive Caucus, EMILY's List, Indivisible and J Street all spent significant sums backing Ramirez, helping her outlast Chicago Alderman Gil Villegas, who had the support of moderate-backing outside groups Democratic Majority for Israel and Mainstream Democrats PAC.

In Chicago's 1st District, Jonathan Jackson, a son of civil rights leader the Rev. Jesse Jackson, will win the Democratic nomination to succeed retiring Rep. Bobby Rush, CNN projects. Jackson, like Ramirez, had support from García, Sanders and the Congressional Progressive Caucus.

The first New York primary day

It was also primary day in New York -- the first of two, this one for statewide contests, after a protracted redistricting process pushed the congressional races into late August.

Senate Majority Leader Chuck Schumer ran unopposed in the Democratic primary, a notable if unsurprising resolution after more than a year of national speculation that he might draw a challenger from the left.

New York Gov. Kathy Hochul faced voters for the first time at the top of the statewide ticket and will win the nomination, CNN projects, putting her on a path to become the first woman elected to the state's top job.

Hochul entered the office last year following Andrew Cuomo's resignation. She was flanked in the primary, on the left, by New York City Public Advocate Jumaane Williams and, on the right, by New York Rep. Tom Suozzi, but remained the favorite throughout the campaign.

Down the ballot, the result appeared to be less certain.

But CNN projects that Hochul's lieutenant governor, former Rep. Antonio Delgado, who took office a little more than a month ago, will be her running mate in November. Delgado was Hochul's second choice for the job, coming aboard last month following the resignation of her first pick, Brian Benjamin, who stepped down after being indicted on federal corruption charges. (He's pleaded not guilty.)

Delgado defeated Ana María Archila, a longtime progressive organizer recruited to run earlier this year by the Working Families Party after she stepped down as co-executive director at the Center for Popular Democracy. Archila, though significantly outraised by Delgado, ran a more active campaign and deep connections from her base in New York City to more progressive enclaves around the state after years of advocacy work. Diana Reyna, a former city council member and deputy borough president in Brooklyn, is expected to finish third.

Hochul will face New York Rep. Lee Zeldin, whom CNN has projected will win the GOP nomination, in the general election. Zeldin, who represents eastern Long Island, had the lion's share of state GOP establishment support, but had to fight through a tense and testy campaign featuring former Trump White House aide Andrew Giuliani, son of Trump ally and former New York City Mayor Rudy Giuliani; businessman Harry Wilson; and former Westchester County Executive Rob Astorino.

Mississippi runoffs

Republicans had three nominations to determine in Mississippi after candidates in each race failed to notch a majority in their June 8 primaries.

Jackson County Sheriff Mike Ezell will win the nomination in Mississippi's 4th Congressional District, CNN projects, unseating incumbent Rep. Steven Palazzo.

Palazzo entered the campaign facing a slew of ethics issues, including alleged misuse of campaign and congressional funds (he has denied any wrongdoing) and criticism over his use of proxy-voting. Still, he finished first in a seven-candidate field earlier this month.

But the opposition consolidated in the Tuesday runoff, likely sending Ezell to Congress from the heavily Republican Gulf Coast district.

In the 2nd District, Brian Flowers and Ronald Eller are vying for a chance to take on Democratic Rep. Bennie Thompson, chair of the House's January 6 select committee.

This story has been updated with additional developments Tuesday.