Sen. Robert Menendez (D-N.J.), who is Cuban-American, blasted the decision, labeling Mariela Castro "a vociferous advocate of the regime and opponent of democracy," according to The Associated Press.
Four Cuban-American lawmakers sent a letter to Secretary of State Hillary Clinton on Thursday protesting the move.
"The administration's appalling decision to allow regime agents into the U.S. directly contradicts congressional intent and longstanding U.S. foreign policy," wrote Reps. Mario Diaz-Balart (R-Fla.), Ileana Ros-Lehtinen (R-Fla.), Albio Sires (D-N.J.) and David Rivera (R-Fla.).
"While the Cuban people struggle for freedom against increasing brutality at the hands of Castro's thugs, the Obama administration is greeting high-level agents of that murderous dictatorship with open arms," they wrote. "It is shameful that the Obama administration would waive the common-sense restrictions in place to appease the Castro dictatorship once again."
Sen. Marco Rubio (R-Fla.), who is also Cuban-American and has been widely rumored to be among the leaders for Romney's vice presidential nomination, likewise slammed the decision as "shameful" in a video statement Friday.
"I think the U.S. government’s decision to grant the daughter of Raul Castro a visa to come to the United States and spread the propaganda of her father’s regime is outrageous and an enormous mistake. Not only that, it sends a terrible message to the democratic movement in Cuba, to those brave people in Cuba who every single day resist and speak out against the tyranny of the Castro brothers," Rubio said.
The Obama campaign returned fire later Friday afternoon, dismissing the Romney criticism as "bluster."
“This is yet another example of Mitt Romney’s campaign trying to score political points to distract from the fact that he has no policy ideas of his own to successfully confront the challenges of the future. The President believes that the promotion of democracy and human rights in Cuba is in the national interest of the United States and that, while maintaining the embargo, decreasing the dependency of the Cuban people on the Castro regime is a means to obtaining the widely-shared goal of a Cuba that respects the basic rights of all its citizens. It is clear that Gov. Romney and his advisors would rather bluster and score political points than say what kind of leader he would be in the world," said Obama Hispanic issues adviser Freddy Balsera.
Romney was campaigning in Florida earlier this week, but returns to New Hampshire on Friday for a campaign event and weekend rest at his home there.
This post was updated at 2:37 p.m.