An effort by Rep. Mario Diaz-Balart to overturn Obama administration rules easing restrictions on travel to Cuba may win congressional approval despite a threatened presidential veto, according to supporters and even some critics.

The Florida Republican’s proposal was initially given little chance of becoming law, especially after President Barack Obama last week vowed to veto it if it reached the White House for his signature.

But as the bill’s possible paths through Capitol Hill became clearer, even some of its critics now say they believe the measure stands a reasonable chance of making it past Congress and even the White House.

“Although we appreciate the president’s veto threat, there is no question that this misguided legislation, due to the way it’s been placed in an appropriations bill, has a good chance,” said former Democratic congressional candidate Joe Garcia.

“I am certainly NOT surprised that this looks like it’s going to pass,” added Mauricio Claver-Carone, director of the U.S. Cuba Democracy political action committee, which supports strong U.S. sanctions on Cuba.

Diaz-Balart’s effort would set Cuba travel restrictions back to their level under President George W. Bush: for Cuban-Americans, only one trip every three years for “family reunifications,” a cap of $1,200 per year in remittances to relatives and a tighter definition of “family.” Restrictions on non-Cuban U.S residents were far tighter.

Under Obama administration policies designed to help the island’s civil society overcome the grip of the Communist government, Cuban Americans can visit Cuba as many times as they wish and send at least $2,000 a year. Travel and remittance regulations for non-Cuban U.S. residents also have been eased.

Diaz-Balart’s proposal has come under withering criticism from some Cuban-Americans and dissidents on the island who argue that it would only add to the distance between Cuban families on either side of the Florida Straits.

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