(CNN) Two key Democrats on the Senate Foreign Relations Committee are signaling they won't back CIA Director Mike Pompeo for secretary of state, a sign that his nomination as the top US diplomat is likely to face a rebuke by falling short of a majority on the panel.

In interviews with CNN, Democratic Sens. Tim Kaine and Jeanne Shaheen -- who sit on the panel and backed Pompeo's nomination to be CIA director -- say they are harboring concerns with the nominee, a clear signal they may vote against him. In addition, Republican Rand Paul also told CNN that the hearing "really solidified" his opposition to Pompeo.

"I voted for him as CIA director and haven't had cause to regret that vote," Kaine told CNN. "But I have serious doubts about whether he's the diplomat that we need right now."

If all three members ultimately vote "no," then Pompeo won't have enough votes to win a favorable recommendation from the committee.

But in an extraordinarily rare move, Senate Majority Leader Mitch McConnell could still bring up the nomination on the floor of the Senate despite the negative vote in the committee. If that would occur, Pompeo would need the support of at least one Democratic senator, given Paul's opposition and the continued absence of Sen. John McCain, who is recovering from brain cancer. And behind the scenes, Pompeo has been working to lock down support from moderate Democrats, including ones in tough races, to push him through on the floor.

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