Just hours after Obama announced that a prisoner swap with the Cuban government for two Americans was the start of a new relationship with the communist country, Republicans began informally kicking around ideas to stop any changes to the U.S.-Cuba relationship.

On the list: deny Obama funds to reopen an embassy in Havana, stall the nomination of a potential ambassador, vote down a bill to open up travel more widely and ignore requests from the White House to lift a decades-old embargo.

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When Republicans control the Senate next year, the party would be in a good position to get some of their plans done. But even if they can’t fully stop Obama, who has some authority to act without Congress, the dispute will provide another opportunity for the president’s Hill rivals, including 2016 likely hopefuls Sens. Ted Cruz and Marco Rubio, to continue to question his use of executive action — a theme Republicans had already planned to take on next year around Obama’s moves on immigration and Obamacare.

“I will do all in my power to block the use of funds to open an embassy in Cuba. Normalizing relations with Cuba is bad idea at a bad time,” Sen. Lindsey Graham (R-S.C.) said on Twitter Wednesday.

In a White House address on Wednesday, Obama said he would direct Secretary of State John Kerry to review’s Cuba’s place on a list of state sponsors of terrorism, reestablish an embassy in Havana and ease travel restrictions. Obama also said the U.S. would increase remittance levels, expand commercial sales and exports.

( Also on POLITICO: GOP livid over Cuba)

“We will end an outdated approach that for decades has failed to advance our interests,” Obama said. “Neither the American nor the Cuban people are well-served by a rigid policy that is rooted in events that took place before most of us were born.”

Republicans will control the Senate starting in January, meaning they will have the power to block presidential nominations. Already a number of influential Republicans vocal on foreign affairs, including Graham, Sens. John McCain (R-Ariz.), Rubio (R-Fla.) and Cruz said they staunchly oppose Obama’s plans.

Obama also called on Congress to peruse legislation that would lift the 50-year embargo against goods and travel to the Cuba. That embargo, launched by President John F. Kennedy, is not solidified by decades of congressional legislation - a fact Obama alluded to in his remarks.

“The embargo that has been imposed for decades is now codified in legislation. As these changes unfold, I look forward to engaging Congress in an honest and serious debate about lifting the embargo,” he said.

But Speaker John Boehner said he would not allow any Cuban-U.S. relations to be revisited in the House.

( Also on POLITICO: Rubio calls out pope on Cuba)

“Relations with the Castro regime should not be revisited, let alone normalized, until the Cuban people enjoy freedom – and not one second sooner. There is no ‘new course’ here, only another in a long line of mindless concessions to a dictatorship that brutalizes its people and schemes with our enemies,” the Ohio Republican said.

Incoming Senate Majority Leader Mitch McConnell (R-Ky.) said he would defer the upper chamber’s response to Cuba policy changes to Rubio, who slammed Obama for threatening U.S. national security concerns.

Already some Republicans are casting doubt on if the Obama administration has the legal authority to roll back some travel restrictions and allow increased numbers of Cuban cigars to be brought into the U.S. Rep. Ileana Ros-Lehtinen (R-Fla.) said action by Obama “may be in direct violation of Helms-Burton that specifically states that all political prisoners must be released and free and fair elections must be held before establishing a diplomatic relationship.”

The incoming chairman of the Senate Foreign Relations Committee Tennessee Republican Bob Corker gave few details on Wednesday on what his panel would do to halt any of Obama’s proposals.

“The new U.S. policy announced by the administration is no doubt sweeping, and as of now there is no real understanding as to what changes the Cuban government is prepared to make. We will be closely examining the implications of these major policy changes in the next Congress,” he said.

Meanwhile Democrats were mixed on their response to Obama’s plans. Sen. Robert Menendez (D-N.J.), the current chair of the Forign Relations Committee was highly critical of Obama’s proposals. But House Minority Nancy Pelosi hailed Obama’s “new chapter.”

“It is clear that policy of isolating Cuba is serving neither the interests of the American people nor the democratic aspirations of the Cubans,” Pelosi said. “We must acknowledge our policy towards Cuba is a relic of a bygone era that weakens our leadership in the Americas and has not advanced freedom and prosperity in Cuba.”