President Barack Obama’s plans to seek a normalization of relations with Cuba split lawmakers, and those on the opposing side vowed to use whatever means available to stand in the way of the policy shift. Mr. Obama said he looked forward to engaging with lawmakers on ways to further his policy aims, but top Republicans signaled they would have little appetite for a rapprochement.

“Relations with the Castro regime should not be revisited, let alone normalized, until the Cuban people enjoy freedom – and not one second sooner,” House Speaker John Boehner (R., Ohio).

For those hoping to halt, or at least slow, the president’s efforts, there are a handful of legislative paths that are could present themselves once lawmakers return to Washington. They fall in three general areas:

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SPENDING BILLS: The most powerful tool available to Congress is its power of the purse: the ability to fund–or more importantly, defund–government programs, initiatives and other policies that lawmakers don’t like. The $1.1 trillion spending bill enacted last week, for example, contains Cuba-related provisions in its roughly 1,600 pages, including a prohibition against funds for U.S. agriculture programs from being used to directly finance or provide assistance to Cuba and a handful of other countries.

Critics of Mr. Obama’s normalization plans have already signaled they plan to use the appropriations process to try to slow the process. Sen. Lindsey Graham (R., S.C.) tweeted on Wednesday that “I will do all in my power to block the use of funds to open an embassy in Cuba.” That’s no idle threat; Mr. Graham is slated to become chairman of the Senate Appropriations Committee’s subcommittee on state and foreign operations next year. That not only puts him in charge of a bill that included $49.3 billion in discretionary spending for  fiscal 2015, but also oversight of the State Department’s budget.

Rep. Kay Granger (R., Texas), who chairs the state and foreign operations subcommittee on the other side of the Capitol, criticized the administration’s decision to act unilaterally.

“Congress has a vital role to play in our country’s foreign policy and how American taxpayer dollars are used,” Ms. Granger said.

Beyond preventing funds for the establishment of a U.S. embassy in Havana, appropriators have yet to tip their hands as to how they might try to use their appropriations power to slow Mr. Obama’s plans. Aides suggested one approach would be for critics to explicitly single out Cuba as ineligible for funds appropriated to various government agencies and programs on a broader scale than is currently employed.

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NOMINATIONS: Another easy avenue available to Cuba critics would be to block or slow Mr. Obama’s nominations to the State Department and other international posts as a protest against the attempt to normalize relations with Havana. The White House is already going to face a tougher process getting its executive branch appointments confirmed under the new GOP-controlled Senate, but the addition of a hot-button political issue such as Cuba could make it harder.

Sen. Marco Rubio (R., Fla.), Cuban-American himself, said as much on Wednesday at a news conference criticizing the Obama administration’s move. “I anticipate we’re going to have a very interesting couple of years discussing how you’re going to get an ambassador nominated and how you’re going to get an embassy funded,” he said.

Like Mr. Graham, Mr. Rubio will be in a position to follow through on his promises. He’s slated to chair a key subcommittee on the Senate Foreign Relations Committee next year, giving him the ability to challenge the White House and State Department in both hearings and when the panel considers nominations.

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EMBARGO ACTION: In his announcement Wednesday, Mr. Obama said he hoped to engage Congress “in an honest and serious debate” about lifting the current embargo that restricts most travel and trade with Cuba. That is not expected to happen any time soon. In fact, strong anti-Cuba lawmakers will want to tighten the embargoes.

The current U.S. embargo dates back to the 1960s and has been cemented into U.S. law through a number of legislative actions over the years. Mr. Obama acknowledged that Wednesday but said he hoped to work with Congress to reverse course.

Critics said the opposite – an attempt to reverse the action – is more likely. Rep. Ileana Ros-Lehtinen (R., Fla.), a vocal critic of the Castro regime, said in a Wednesday statement that it was possible that the actions by the White House violated a number of Cuba-related laws passed previously by Congress.

“The White House attempts to normalize relationships with Cuba without the approval of Congress 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,” she said.

The biggest challenge to this approach would be Mr. Obama himself. While the Republican-led Congress could seek to pass legislation targeting the normalization effort, the president would probably veto anything lawmakers were able to pass. Additionally, with bipartisan support for the White House’s plan to establish diplomatic ties, it’s unclear whether any punitive legislation could even make its way through both the House and Senate.