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Texas state House Democrats left the state Monday in an effort to block Republicans from passing a restrictive new voting law in the remaining 27 days of the special legislative session called by Gov. Greg Abbott.

Two chartered planes carrying the majority of the Democrats who left Texas for Washington, DC, landed at Dulles International Airport on Monday evening, a source familiar told CNN. They have largely kept their planning secret because they can be legally compelled to return to the state Capitol and believed law enforcement could be sent to track them down, two sources familiar with the Democrats’ plans had told CNN earlier Monday.

The group is “hoping” to meet with US Senate Democrats, according to a source familiar with their plans.

Their move places Texas at the heart of the national fight over voting rights, with GOP state lawmakers turning former President Donald Trump’s lies about widespread voting fraud into a push for new laws that limit mail-in voting, early voting and more.

Already this year, Republican-controlled states including Florida, Georgia and Iowa have enacted restrictive new voting laws. Democrats in Congress have pushed measures that would expand access to the ballot box nationwide – but GOP opposition in the Senate has kept them from clearing the 60-vote threshold necessary to break a filibuster.

In Texas, minority House Democrats walked out of the final hours of this year’s legislative session, blocking Republicans from approving Senate Bill 7 – the controversial measure that would have made casting mail-in ballots harder; banned drive-thru voting centers and 24-hour voting – tactics Harris County, the home of Houston, used in the 2020 election; empowered poll watchers, made it easier for courts to overturn election results; effectively outlawed Black churches’ “souls to the polls” get out the vote push and more.

Abbott, the Republican governor who is seeking a third term in 2022, called a 30-day special legislative session, saying that “election integrity” would be one of his priorities. Majority Republicans in the House and Senate in recent days unveiled bills that closely mirrored SB 7.

State House and Senate committees advanced those bills after hearing opposition in hours-long hearings over the weekend.

The Democrats’ move raises questions about their objectives – whether they are seeking to block any new voting laws altogether or push Republicans to strip their measures of what Democrats see as the most objectionable elements – and how Republicans will try to force Democrats back into the House.

While driving from Texas to Washington on Monday evening, Democratic state Rep. John Bucy told CNN’s Erin Burnett on “OutFront” that Texas is “already the hardest state in the nation to vote. And this would make it even harder.”

“Our secretary of state office in Texas told us that our elections ran smoothly, securely and were a success. So you have to question: What is the problem these bills are trying to solve?”

Bucy added that, while in Washington, he and his colleagues will seek to pressure Congress to act because “this isn’t just Texas.”

“All over the South in Republican states we’re seeing voter suppression bills. So we need Congress to pass the For the People Act, and the John Lewis Voting Rights Act to make sure all Americans’ rights to vote are protected.”

Republicans were critical of the Democrats’ decision – but did not say what their next move would be.

State House Speaker Dade Phelan said in a statement that the House will use “every available resource under the Texas Constitution” to secure a quorum of two-thirds of the chamber’s members.

The governor, in a statement, said the “Texas Democrats’ decision to break a quorum of the Texas Legislature and abandon the Texas State Capitol inflicts harm on the very Texans who elected them to serve.”

US Sen. John Cornyn, a Texas Republican, said of the move: “It’s not very Texan. You stay and you fight – you don’t run away.”

However, national Democratic figures backed the Texas House members’ move to break quorum and flee the state.

“I applaud them standing for the rights of all Americans and all Texans to express their voice through their vote, unencumbered. I will say that, that they are, they are leaders who are marching in the path that so many others before this, when they fought and many died for our right to vote,” Vice President Kamala Harris said in Michigan.

Former Rep. Beto O’Rourke, who came close to winning a Senate seat in Texas in 2018 and is a potential 2022 gubernatorial candidate, testified at a state legislative hearing on the GOP bills over the weekend and raised money for Texas House Democrats’ effort on Monday.

“These Texas Democrats are the courage the country needs right now,” he said on Twitter. “They give us a fighting chance to pass the For the People Act – and save our democracy.”

This story has been updated with additional developments Monday.

CNN’s Jessica Dean and Manu Raju contributed to this report.