Conservatives opposed to the Export-Import Bank are trying to dial up pressure on Majority Leader Mitch McConnell to prevent a vote on restarting the moribund Export-Import Bank.

Ken Cuccinelli, president of the Senate Conservatives Fund, accused McConnell, R-Ky., of "pretending to oppose Ex-Im."

McConnell has repeatedly voted against Ex-Im, but he has promised Washington State senators that he would allow a floor vote on renewing the agency, which has been in liquidation since July 1.

Sen. Ted Cruz, who joined Cuccinelli and other conservatives at a press conference Wednesday morning, also called on McConnell to block all floor votes on Ex-Im. "This comes down to two men," the Texas Republican said at the same press conference Wednesday morning, naming McConnell and House Speaker John Boehner.

Because Ex-Im is now in liquidation, bringing it back to life would require both chambers to pass a bill restarting the agency, plus a signature from the president. Ex-Im opponents — and McConnell identifies as one — could permanently kill the agency by simply blocking floor votes on any measure to bring the agency back to life.

"What they're asking for is not something we have the ability to do," McConnell's office replied. This would require McConnell resurrecting the practice of the Harry Reid era and blocking all floor amendments.

By the reckoning of Heritage Action, a conservative group that has helped lead the charge against Ex-Im, this is surrender by McConnell. In a July 1 memo, Heritage Action pointed out, "To date, Majority Leader McConnell has not allowed a non-budget amendment to pass that he and a majority of his conference opposed." Those two amendments were supported by most Republicans including the relevant committee chairmen.

Most Senate Republicans oppose Ex-Im, including Banking Committee Chairman Richard Shelby.

Neither Cruz nor Utah Sen. Mike Lee, who also took part in the press conference, would endorse Cuccinelli's charge that McConnell is only pretending to oppose Ex-Im. McConnell voted against reauthorizing the agency twice in 2012 and once this June.