The House is due to hold a second vote to fill the vacant speaker's chair when it convenes at 11 a.m.
It is not clear whether Jordan, a close ally of former President Donald Trump, will fare better in a second vote.
At least one Republican who voted against him on Tuesday, Representative Doug LaMalfa, said he would vote for Jordan on the second ballot.
"He's the only viable candidate we have," Republican Representative Thomas Massie told reporters.
Democrats, meanwhile, are pressing for a bipartisan compromise that could result in more powers for Republican Representative Patrick McHenry, who is acting as temporary speaker.
Persons:
Jim Jordan, Jordan, Kevin McCarthy, Donald Trump, Doug LaMalfa, Ken Buck, Jordan's, Thomas Massie, Patrick McHenry, Hakeem Jeffries, John Boehner, Joe Biden's, David Morgan, Moira Warburton, Katharine Jackson, Makini Brice, Andy Sullivan, Scott Malone, Grant McCool
Organizations:
U.S . House, Republican, Republicans, New Republican, U.S . Rep, U.S, Capitol, Democratic, Caucus, Committee, Biden, White, Thomson
Locations:
U.S, East, Ukraine, Washington