The new session of Congress convenes Tuesday, with a Republican majority aiming to derail some of President Obama’s signature policies. For some lawmakers, one target includes the normalization of U.S.-Cuba relations announced less than three weeks ago.

Congress won’t be able to do much to block the easing of trade or travel restrictions between the U.S. and Cuba, but some legislators have threatened to thwart the president’s goals through two primary channels: Blocking Senate confirmation of an ambassador to Cuba and obstructing funding for a U.S. embassy in Havana.

Any nominee for U.S. ambassador to Cuba would have a “snowball’s chance in hell” of getting confirmed by the Senate, Sen. Lindsey Graham, R-S.C., said on CBS’ "Face the Nation" last month. Rep. Marco Rubio, R-Fla., and Sen. Robert Menendez, D-N.J., have also openly criticized the president’s move to resume diplomatic relations with Cuba, with Rubio vowing to block any confirmation and Menendez predicting a “very difficult” confirmation process for any nominee.

Menendez is the outgoing chair of the Senate Foreign Relations Committee, which is responsible for clearing nominees to face a full confirmation before the Senate. Sen. Bob Corker, R-Tenn., takes over as chairman in the new session. So far, he’s refrained from opining on the issue, saying only that the next Congress would be “closely examining the implications of these major policy changes.”

Despite the Republican majority in the new Congress, attitudes on U.S.-Cuba relations aren’t strictly cut along party lines. Republicans such as Sens. Jeff Flake, R-Ariz., and Rand Paul, R-Ky., have supported the thaw, so it’s not entirely clear how tough the road may be in getting an ambassador confirmed.

Although White House officials haven’t divulged names under consideration for ambassador, Jeffrey DeLaurentis, a career foreign service officer and the current U.S. chief of mission at the U.S. Interests Section in Havana, could be a top contender for the spot. He’s set to become the U.S. charge d’affaires for the embassy in Cuba – which functions as an ambassador when there isn’t one – putting him in a prime position for a nomination.

In a profile of DeLaurentis at the Daily Beast, several foreign affairs analysts painted him as a highly capable, committed professional well-suited to undertake the enormous task of normalizing U.S.-Cuban diplomatic relations. “He is exceptionally well qualified to manage this historic and positive change in relations for the foreseeable future,” Brookings senior fellow Ted Piccone told the website.

But regardless of who eventually receives the nomination, Cuba’s human rights record remains a sore sticking point for some lawmakers, particularly those from South Florida, who say the U.S. shouldn’t engage with the island while the Communist regime of Raul Castro remains in power. That sentiment is largely held by Cuban exile communities in Florida, but the younger generation of Cubans does not appear as focused on Cuba's human rights record. It has, for example, increasingly supported overturning the U.S. embargo. The U.S. State Department criticized Havana’s move last week to detain 50 political dissidents protesting outside government headquarters, which could provide fresh fodder for Congressional critics to speak out against the president’s move. (The government freed some of the activists shortly afterward.)

Meanwhile, some members of Congress have also threatened to block any funding needed for a U.S. embassy in Havana. The U.S. diplomatic presence in Cuba currently operates in a building in Havana under the “special protection” of the Swiss embassy. But White House Press Secretary Josh Earnest said last month that it was not yet clear if re-establishing the building as an embassy would require any additional funds

Congress also represents the final hurdle to ending the U.S. embargo on Cuba, which can only be lifted through legislation. That would be the most challenging battle of all if lawmakers even tried to take it on.