MIAMI (AP) — The door for travel to Cuba cracked open during President Barack Obama’s first term.

Cuban-Americans can now visit family on the island as often as they like. Americans can travel legally as part of an academic or religious trip.

Perhaps it’s for this reason that Obama’s standing with the Cuban-American community in Florida stayed largely steady on Election Day, even though the modest openings with Cuba have riled some of South Florida’s more conservative exiles. Exit polling showed that 49 percent of Cuban-Americans voted for the Democrat, roughly the same percentage as four years ago.

At the same time, Florida voters sent to the House a Cuban-American Democrat from Miami who supports Obama’s expansion of travel and remittances to Cuba while still favoring the 50-year-old embargo that limits American trade with the communist country. Joe Garcia defeated Republican Rep. David Rivera, who was implicated in a campaign finance scandal and had supported a traditional, isolationist stance toward Cuba.

The victories by supporters of looser restrictions on Cuba travel illustrate changing attitudes of Americans who hail from the island nation: They seem to be less resistant to politicians who promote travel to Cuba and more focused on more traditional American concerns such as the economy, rather than Cuba policy. Those shifting attitudes could have implications for U.S. policy toward Cuba in the next four years, as well as how presidential candidates and politicians approach Cuban-Americans in Florida, an important swing state, in the future.

There are plenty of other impediments, chiefly the continued detention of U.S. contractor Alan Gross by the Cuban government, which could delay a further easing of restrictions with Cuba. Gross was arrested in 2009 while working as part of a democracy-building program; he’s now serving a 15-year prison term for bringing restricted communications equipment into Cuba.

But analysts argue that the political environment is ripe for reducing restrictions on the Cuba travel policy, and they point to both the election outcome and changes on Capitol Hill among Florida’s Cuban-American delegation.