Both the Republican and Democratic Senate leaders said they want a vote on reauthorizing the bank, with Majority Leader Harry Reid, D-Nev., saying he wants floor consideration before the bank's authorization expires Sept. 30.
"The Export Bank is so very, very important to the country," Reid told reporters on Tuesday.
And Senate Minority Leader Mitch McConnell, R-Ky., said he supports bringing the a bank reauthorization measure to the Senate floor for debate, even though he has not decided whether to vote for it.
McConnell opposed the last reauthorization of the bank in 2012, joining 20 other GOP opponents in the Senate.
"I have no problem whatsoever with the matter being scheduled," McConnell said Tuesday. "It should be scheduled."
So far, the Senate is emerging as the potential lifeline for the bank, which guarantees and provides loans to enable foreign companies to purchase U.S. goods.
The bank, which operates as a federal agency, has existed since the 1930s and has been reauthorized repeatedly without much opposition from Congress.
In recent years, however, conservative Republicans and conservative groups have increasingly called for an end to the bank, declaring it a form of corporate welfare shouldered by taxpayers.
The drumbeat has grown louder in reaction to a Wall Street Journal report that four Ex-Im employees have been removed for allegedly receiving gifts or steering loans to certain businesses, suggesting a pattern of crony capitalism.
"I don't want to reauthorize it," Rep. Jason Chaffetz, R-Utah, told the Washington Examiner. "It's not necessary and it creates unfair competition."
The threat to the bank's renewal grew exponentially on Sunday when incoming House Majority Leader Kevin McCarthy, R-Calif., signaled he won't take it up this year.
The Ex-Im Bank's lending, McCarthy said on "Fox News Sunday," "is something government does not have to be involved in," adding, "The private sector can do it.
On Tuesday, House Speaker John Boehner, R-Ohio, was noncommittal, even though the House overwhelmingly reauthorized the bank in 2012 and Republicans face pressure from the U.S. Chamber of Commerce and other big-business groups who back the bank.
"Some people believe that we shouldn't have it at all, others believe that we should reauthorize it with significant reforms," Boehner said, describing the position of the members in his conference. "And we're going to work our way through this."
Hensarling is chairman of the House Financial Services Committee, which will play a key role as the committed of jurisdiction in deciding whether to reauthorize the bank.
Hensarling strongly opposes re-upping the bank, saying it exposes taxpayers to risky loan guarantees that private companies are unwilling to make. Hensarling has pointed out that the bank provided loan guarantees and loan assistance for the now-defunct solar company Solyndra as well as Enron Corp.
"Hensarling is leading the charge to kill it, so I don't even know if it will get out of committee," said Rep. Matt Salmon, R-Ariz., who backs the bank's reauthorization. "It may not even come to the floor for a vote. It's all very tenuous."