Washington — For months, the Trump administration has sought to terminate Temporary Protected Status (TPS) programs for immigrants from several countries in Latin America and Africa, though its efforts have been hampered by court rulings. But two Florida congressmen believe there's a good chance President Trump will support their newly-unveiled legislation to extend TPS protections to Venezuelans.

"If there is a country that might get TPS approved by the White House, it would be Venezuela," Rep. Darren Soto, a Democrat, told CBS News. "Because this would enhance the sanctions that the White House has already put forward."

On Thursday, Soto and Rep. Mario Díaz-Balart, a Republican, introduced the Venezuela TPS Act of 2019, a legislative project that has been months in the making. If enacted, it would allow Venezuelans living in the U.S. who have fled the country's repressive government and collapsing economy to qualify for TPS protections and work permits.

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"This is not a traditional immigration bill," Díaz-Balart told CBS News. "This is the recognition of specific circumstances that the administration has recognized." The Cuban-American legislator said that by backing the legislation, the White House would remain in lockstep with its "aggressive" stance against the government of Venezuelan President Nicolás Maduro.

The Trump administration has imposed several economic sanctions on Maduro's government and companies with ties to the Venezuelan leftist leader, who has consolidated power by stacking the judiciary with his allies, overhauling the legislative branch and maintaining a tight grip on the military. Mr. Trump included Venezuelan government officials in the third version of his travel ban, which the Supreme Court upheld last summer. In addition to purportedly discussing a military coup with dissidents, the White House is reportedly considering recognizing the chief opposition leader in the country, National Assembly President Juan Guaido, as Venezuela's legitimate head-of-state.

Granting TPS protections to Venezuelans fleeing Maduro's authoritarian rule, Díaz-Balart said, would put more pressure on his regime and further isolate the South American leader, who a dozen Latin American foreign ministers said should hand over power two weeks ago.

"You're talking about a dictator who has not only stolen, in essence, the wealth of the country for personal gain and to use it for nefarious purposes around the world, but has also used the country's wealth to frankly repress and to murder its own people," Díaz-Balart added.

Oil-rich Venezuela was once considered one of Latin America's wealthiest nations. But under Maduro — who replaced Hugo Chavez, another leader accused of authoritarian tendencies, in 2013 — economic turmoil, skyrocketing inflation, food shortages, mounting crime and government corruption have plunged the country deep into a socio-political crisis.

To stifle discontent over the floundering economy, weakened further by international sanctions and plummeting oil production, Maduro has resorted to political oppression and, allegedly, even torture. Recent elections in the country have been denounced by United States and the international community as unfair and rigged. The Organization of American States (OAS) recently passed a resolution agreeing not to recognize the legitimacy of Maduro's new term, which began on January 10.

The dire situation has prompted more than 2.3 million Venezuelans to flee the country since 2014 — an exodus Human Rights Watch called "the largest migration crisis of its kind in recent Latin American history." More than one million Venezuelans have fled to neighboring Colombia, hundreds of thousands to Peru, Ecuador and other countries in the region — and more than 72,000 have come to the U.S.

Díaz-Balart said it is "the largest refugee crisis in the history of this hemisphere."

"The question is: Is it reasonable to say that folks that are in the United States should be sent back to that country?" he added.

The legislation from Diaz-Balart and Soto would make Venezuelans eligible for TPS if they came to the U.S. after early 2013 and have no legal status. A window for new applications would be open for 18 months from the day the bill is signed into law.

Soto said Sens. Marco Rubio, R-Florida, and Bob Menendez, D-New Jersey, are working on a similar bill in the Senate. Soto added that Venezuelans in the U.S. desperately need this immigration relief.

"We can't just leave them in limbo," Soto said. "This bill will achieve the goal that we set out to accomplish, which is to have well-need relief for these political refugees who face death and destruction back home."

It is not clear if the Trump administration will ultimately support the bill. A spokesperson for the Department of Homeland Security (DHS), which designates TPS protections for foreign nationals, told CBS News the agency does not weigh in on pending legislation.

Under Mr. Trump's tenure, DHS announced the eventual termination of TPS protections for more than 250,000 immigrants from El Salvador, Honduras, Sudan and Haiti, but a federal judge blocked the decision in early October.

Still, Soto signaled he was fairly optimistic about the possibility of the White House backing the bill. "If they would ultimately approve any new TPS, this would be the one," he said.