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.
Politics shouldn’t be about owning the other side. The Dems should not vote outside their party unless they have a deal to do so.
However, yes, the Dems could help to vote in a moderate speaker. They should negotiate concessions to do so. Doing so freely would be bad politics. It would give the far right fodder to rile up their base. It gives the moderate Republicans no reason to fight back against the far right and gives the Dems no win a part from the Republicans enacting their policies, which often is against the Dems policies.
Purposely inflaming the far right only emboldens them. This is one time the high ground actually works to penalose the far right and make them less effective.