By Alex Rogers, CNN

(CNN) -- Florida Democratic Rep. Stephanie Murphy is seriously considering a run against Republican Sen. Marco Rubio in 2022, launching a listening tour on issues including the pandemic, "managing misinformation," fighting climate change and for social justice.

Murphy, co-chair of the centrist Blue Dog Coalition of House Democrats, hopes that by emphasizing a bipartisan background she can appeal to a state that has elected Republicans to the Senate in 2016 and 2018 and twice supported former President Donald Trump. Murphy has hired Lauren Calmet, the former political director of the Florida Democratic Party, to organize her new initiative, called "Cast Forward," and has talked with Georgia's Stacey Abrams about how to rebuild Florida's party's infrastructure.

"I firmly believe that Florida is not a red state; it's a hard state," Murphy told CNN in an interview. "You have to have the right money, message, and machine to compete and after a few disappointing election cycles, it's clear that we've fallen short."

She added she wanted to lay "the foundation for Democrats winning in 2022."

When Murphy was a baby, her family fled Communist Vietnam and was rescued by the US Navy. She emphasized her story as a refugee in a new video, saying that her parents "sacrificed an awful lot in escaping socialism" and said that she is "a proud capitalist and a proud Democrat" fighting for a fairer economy.

The comments indicated she took to heart the 2020 loss of two House Democrats representing South Florida, former Reps. Donna Shalala and Debbie Mucarsel-Powell, whom Republicans attacked as socialists who were weak on Cuba and Venezuela.

In the interview, Murphy also previewed a potential attack against Rubio, a two-term senator.

"I think the challenge for Rubio is that he's made it apparent to everybody that the only person he cares about is himself," she said. "He'll do anything or say anything to stay in power and I think that's unfortunate."

In response, a Rubio campaign spokesman touted Rubio's accomplishments, noting that the senator helped craft the Paycheck Protection Program last year to aid small businesses hit hard by the pandemic, helped expand the child tax credit in 2017 and secured millions for Everglades restoration. The spokesman also noted that the Lugar Center rated him one of the top 10 bipartisan senators in 2019.

"I'm very proud of our record," said Rubio on Thursday. "I would stack it up against anybody, including her."

Murphy also sharply criticized Republicans who supported Trump's effort to challenge the 2020 election, and his urging of Congress to vote against its certification. Rubio was quiet about his position up until the vote, but supported the certification. After the attack on the US Capitol, he said that the mob was "lied to by politicians" who asserted that former Vice President Mike Pence had the power to overturn the election. Florida GOP Sen. Rick Scott, the chairman of the National Republican Senatorial Committee, voted against certification. Murphy said she was also considering a run against him in 2024.

"I fled a communist country. I deeply appreciate the fact that I get to live in a democracy," Murphy told CNN. "The future of our democracy depends on elected officials and the good people of this country to stand up for it. And you've seen Republicans, and you've seen Rubio, support Trump's big lie for months. And I think they did so because they chose their own political future over the future of our democracy."

In 2016, Murphy defeated 24-year GOP Rep. John Mica. But her district in the Orlando suburbs may be redrawn by the Republican state legislature in the coming months. She said she was "less worried" about her district changing and more focused on the "disenfranchisement of Floridians all across the state."

GOP Gov. Ron DeSantis and Republican state legislators have introduced proposals that will make it harder to vote by mail, warning of potential voter fraud, even though the state's 2020 election worked smoothly and there was no evidence of widespread fraud in the state.

This story has been updated Thursday with comment from Rubio's spokesman.