WASHINGTON — President Obama’s plans for a history-making trip to Cuba drew hopeful cheers in Havana on Thursday but equally emphatic condemnation from many U.S. lawmakers and Republican presidential candidates, who accused the president of rewarding a “dictatorial regime.”

Jeb Bush called the plans “appalling.” Florida Rep. Ileana Ros-Lehtinen, born in Havana, deemed Obama’s March 21-22 visit “absolutely shameful.” New Jersey Sen. Bob Menendez – a member of Obama’s party – accused him of ceding U.S. leverage to the communist nation 90 miles south of Florida.

“The president is again prioritizing short-term economic interests over long-term and enduring American values,” said Menendez, another Cuban-American. He likened Obama’s rapprochement with Cuba to his nuclear deal with Iran.

Not so, said Obama, who pledged to press President Raul Castro on human rights and other thorny issues during their sit-down in the Cuban capital. The White House said pointedly that it had put Castro’s government on notice that Obama would also meet with dissidents and activists –a precondition the president had laid out for a visit.

“We still have differences with the Cuban government that I will raise directly,” Obama said as he announced the visit on Twitter.

The trip will mark a watershed moment in U.S.-Cuba relations, making Obama the first sitting U.S. president to set foot on the island in nearly seven decades. The U.S. was estranged from the communist nation for over half a century until Obama and Castro moved toward detente more than a year ago.

Since then, the nations have reopened embassies in Washington and Havana and moved to restore commercial flights, with a presidential visit seen as a key next step.

Yosvany Martinez, a 36-year-old government parking attendant in Havana, said he’d seen changes in his country since the thaw in relations: more tourism and happier people. But Cubans are still struggling economically, he said.

“This visit for me and for all Cubans will be an open door to what we need, which is that they finally lift the blockade, which is what hurts us,” Martinez said.