The Ohio Republican faced opposition from 22 fellow Republicans in the second round of voting on Wednesday, two more than he faced on Tuesday.
Facing such opposition, Mr Jordan's chances of becoming the next House speaker appear to be almost non-existent.
Republicans have been unable to elect a speaker since ousting Kevin McCarthy more than two weeks ago. That has caused paralysis in the US legislature, with lawmakers unable to respond to the Israel-Gaza war, debate on continued assistance for Ukraine and work to avert a government shutdown that is less than a month away.
With Mr Jordan running out of options, lawmakers from both sides have been considering alternative solutions.
House Minority Leader Hakeem Jeffries said it is time for Republicans to work with Democrats to reopen the chamber, although such a scenario at this stage seems implausible.
“The Republicans are unable to function right now,” Mr Jeffries said.
When asked about such an idea, Mr Jordan told reporters: “No one in our conference wants to see any type of coalition government with the Democrats.”
The conversation has also shifted to bestowing speakership powers to Patrick McHenry, Republican US Representative from North Carolina, who is currently serving as speaker pro tempore.
That idea has received the backing of two former Republican House speakers, Newt Gingrich and John Boehner.
But former president Donald Trump has stood by his endorsement of Mr Jordan. Speaking to reporters outside his civil fraud trial in New York, Mr Trump said he still believes the Republican politician would secure the votes needed to win.
Mr Jordan has been one of Mr Trump's fiercest defenders, backing the former president's bogus fraud claims after the 2020 election. He also voted to overturn the electoral college count results for Arizona and Pennsylvania hours after Mr Trump's supporters stormed the Capitol.