Despite intense lobbying behind the scenes, 20 Republicans refused to back the right-wing Ohio congressman.
The Trump ally abandoned plans to hold a second vote until Wednesday morning.
The lower chamber of Congress has been leaderless since an unprecedented vote to oust Kevin McCarthy 15 days ago.
Without a Speaker, the House is unable to pass any bills or approve White House requests for emergency aid. That includes potential help for Israel amid its war with Hamas.
Mr Jordan earned 200 votes in the first ballot on Tuesday, but he needs 217 - indicating majority support in the chamber - to secure the Speaker’s gavel.
The Democratic nominee, Hakeem Jeffries of New York, earned 212 votes, all from his fellow colleagues in the minority party.
Mr Jordan vowed to “keep working” and expressed confidence he would ultimately emerge victorious.
It might even be an actual death sentence.
It only takes one lunatic with a gun who takes the traitor rhetoric seriously to kill someone. And look how crazy they’re getting with people not voting for a republican. Actually voting for a democrat would magnify that massively.