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(CNN) —  

Republican Kentucky Sen. Rand Paul said Wednesday that he intends to oppose President Donald Trump’s nominations of Mike Pompeo as secretary of state and Gina Haspel as the next CIA director, complicating their confirmation process in the Senate where Republicans have a very slim majority.

“I’m perplexed by the nominations of people who loved the Iraq War so much they advocate for war with Iran,” Paul told reporters on Capitol Hill in explaining his opposition to the nominees.

The announcement doesn’t necessarily block the pair’s paths to confirmation. Paul sits on the Senate Foreign Relations Committee, where Republicans hold a one-seat advantage, so if Paul carries out his threat to vote “no” on Pompeo – and all Democrats vote against him – Senate Republican leaders would need to decide if they would move the nominations to the floor without committee approval.

Senate Foreign Relations Committee Chairman Bob Corker, a Tennessee Republican, said that nominees can be reported out of committee for a floor vote with or without a recommendation – and even with a negative recommendation.

“But let us play it out,” he said. “I don’t like to prognosticate.”

Republicans hold a narrow 51-49 advantage in the Senate, so Paul’s opposition – and possible opposition to Haspel from Arizona GOP Sen. John McCain – means Republicans might need to rely on some support from Democrats.

Democratic aides said it was too early in the process to know if any Democrats will back either nomination. Two senators who previously voted to approve Pompeo for CIA director voiced concerns Wednesday over his nomination to the new position.

About Pompeo and Haspel, Paul said at his news conference their support for the Iraq War and Haspel’s “joyful glee” of waterboarding prompted his move.

“To really appoint the head cheerleader for waterboarding to be head of CIA, I mean, how could you trust somebody who did that to be in charge of the CIA,” he said. “To read of her glee during the waterboarding is just absolutely appalling.”

Paul’s comments are a reference to Haspel being a CIA veteran who was intricately involved in the execution of George W. Bush-era CIA interrogation programs, including those carried out at a “black site” prison she reportedly ran. Haspel oversaw the torture of a terror suspect and her name was on a cable giving instructions to destroy video evidence documenting their interrogations, according to The New York Times.

Paul said he has not spoken to the President about his opposition to Pompeo and Haspel, and that while he does support the President and his policies, “Most of the people being appointed are still in favor of Iraq War,” Paul said. “These are the crazy neo conservatives.”

Paul noted that McCain has also voiced some misgivings, but wouldn’t say if he believes the ailing senators would join him in voting against the nominees.

However, “If he were to say no, it might be enough” to kill the nomination.

Republican Rep. Liz Cheney of Wyoming accused Paul of “sympathizing with terrorists” over his opposition.

“Gina Haspel has spent her career defending the American people and homeland. @RandPaul is defending and sympathizing with terrorists,” she tweeted.

Florida Republican Sen. Marco Rubio, a member of the committee, predicted both Haspel and Pompeo will be confirmed and added that shoring up stability at the top of the State Department needs to happen quickly.

“It’s a very important position.” Rubio said about the secretary of state role. “I don’t think the country is at the stage now where it can afford to go for months without stability there. That is a vacancy that needs to be filled. My sense is that irrespective of the vote in committee, it will be brought to the floor for the whole body to weigh in.”

Where key committee Democrats stand

Democrats also highlighted their issues with Pompeo on Wednesday.

New Hampshire Sen. Jeanne Shaheen, one of two Democrats on the Senate Foreign Relations Committee that voted last year to confirm Pompeo to be CIA director, told CNN she now has “concerns.”

“What does he propose for a solution in Syria?” she asked. “How is he going to support our diplomatic efforts and negotiations on North Korea? What’s he going to do about State Department budget and personnel? Is he going to lift the hiring freeze? I think there are a whole list of things that I am very worried about.”

“I’m going to wait and give Mike Pompeo the opportunity to answer those kinds of questions and see what he has to say,” she added.

Sen. Tim Kaine of Virginia, the other Democrat on the committee who voted a year ago for Pompeo, told CNN on Wednesday he has “a lot of concerns” about elevating him to be secretary of state.

“I have very serious concerns because chief diplomat is a very different position than being head of the intel agency,” Kaine said in an interview in the Capitol. “His statements about a number of things make me really worried about whether he will bring the right philosophy to the job.”

While GOP leaders could still move the nomination to the full Senate for a vote – where Pompeo might be able to get at least 51 votes to be confirmed – failing to be approved by the committee could politically damage him, especially when an influential Democrat like Kaine who once backed him turns negative.

“Opposition to the Iran deal is one thing. That wouldn’t slow me down,” Kaine said. “But his notion, ‘oh you know, a couple of thousand sorties, we could wipe them out with all our coalition allies.’ I don’t think we need more fire and fury in the secretary of state’s office.”

Kaine was referring to a 2014 comment Pompeo made to a roundtable of reporters as the Obama administration and allies were in the final days of talks over curbing Iran’s nuclear program.

Pompeo said that it would take “under 2,000 sorties to destroy the Iranian nuclear capacity. This is not an insurmountable task for the coalition forces.”

Kaine said he has not made a final decision about how he will vote.

“I want to listen to the hearings. But I have a lot of concerns,” he said.

UPDATE: This story has been updated after the New York Times issued a correction stating that Haspel did not oversee the torture of Al Qaeda suspect Abu Zubaydah who was waterboarded 83 times in one month.

CNN’s Gregory Krieg and Maegan Vazquez contributed to this report.