A new national poll released on Monday shows that 6 in 10 Republicans support Cuban engagement, which means expanded travel and trade.
The poll released by Engage Cuba, a pro-engagement lobbying group, surveyed 2,000 people.
According to the poll, a move to tighten restrictions on travel and trade would be unpopular with President Donald Trump's Republican base.
"The political and personal interests of two members of Congress should not outweigh the will of the American people and the best interests of Cubans on the island," Engage Cuba president James Williams said.
Williams was talking about U.S. Rep. Mario Diaz-Balart, R-Florida, and U.S. Sen. Marco Rubio. R-Florida, who are said to be in Trump's ear over Cuba policy.
Unconfirmed reports said the White House is thinking of reducing the number of visits to Cuba a person can make to one a year.
"Until 2009, Cuban-Americans were only allowed to visit the island once every three years. Returning to similar travel regulations would be counterproductive, cruel, and do nothing to improve human rights," Giancarlo Sopo of the CubaOne Foundation said.
In light of possible changes toward Cuba, Amnesty International is weighing in on the issue, opposing any rollbacks.
"More travel, more communications access and more dialogue with Cuba are the way forward for human rights in Cuba," said Marselha Gonçalves Margerin, advocacy director for the Americas at Amnesty International.
Trump is scheduled to travel to South Florida this week, where he is expected to announce his new Cuba policy.