Republican Rep. Jim Jordan is pressing ahead with his speaker bid despite facing stiff opposition from within his own party and no clear path to win the gavel.

The House is gearing up for another showdown on the floor Friday with a third speaker vote expected, the latest sign that the Ohio Republican is not backing down even though he lacks the 217 votes needed to secure the speakership. There have been two failed votes so far.

As Jordan works to inject some life back into his flailing speakership bid, three sources told CNN he has made some progress with a small bloc of holdouts: New York Republicans.

If Jordan does win them over, that would still not be nearly enough to secure the speakership, given that 22 Republicans voted against him on the second ballot and more are expected to oppose him on the third ballot. But Jordan is hoping to show some sign of progress ahead of the next vote planned for Friday.

Unlike the other holdouts, the New Yorkers have specific asks and priorities that are pertinent to their districts, such as the state and local tax deduction.

But others are opposed to Jordan based on principle and are dug in as threats against them continue -- a sign of the uphill climb he is still facing. Jordan met with holdouts on Thursday only for several to emerge from the meeting saying their minds had not been changed.

Some Republicans who oppose Jordan have decried what they described as a pressure campaign against them by allies of the Ohio Republican. And several Republicans who opposed Jordan's speakership bid have said they experienced angry calls, menacing messages and even death threats since casting their votes. Jordan has condemned the threats.

A closed-door House GOP conference meeting on Thursday turned heated, multiple sources told CNN. Some members encouraged Jordan to drop out of the race. There was also an emotional discussion over the threats some Jordan holdouts are facing. Later, members leaving the meeting described it as an airing of grievances with tensions running high.

The House remains effectively frozen as long as there is no elected speaker -- a perilous situation as Congress faces an impending government funding deadline and the threat of a shutdown.

The speaker vacuum triggered by the historic ouster of Kevin McCarthy led by a bloc of hardline conservatives also comes as Israel is at war with Hamas and Ukraine fights a war against Russian aggression.

The battle for the speakership has now dragged on for more than two weeks with no end in sight.

Some Republicans looking for a way to break the impasse have suggested expanding the powers of interim Speaker Rep. Patrick McHenry -- a controversial move that would put the House even further into uncharted territory. But there is widespread opposition within the Republican conference to the idea.