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(CNN) —  

Nancy Pelosi’s bid to become speaker of the House is becoming more complicated, as 17 Democrats have now signed a letter saying they won’t vote for her on the House floor, according to four sources with knowledge of the matter.

If these Democrats stick to this pledge, the California Democrat, who is currently the leader of her party in the House, may not have the votes to become speaker. In addition to the 17, five additional Democrats have pledged not to support her on the floor but have yet to sign the letter, one of the sources said.

The goal of the Pelosi critics is to force her out of the speaker’s race by convincing her she does not have the votes to win. But Pelosi and her allies reject that notion and are confident of their chances, saying she will call their bluff on the floor.

Pelosi first needs to win a majority of the House Democrats to win the caucus nomination on November 28. Then, she needs to win a majority of House members who vote for a candidate – likely 218 – and can’t afford to lose too many Democrats on the floor.

Democrats are poised to hold at least 227 seats in the new Congress compared to 200 for Republicans, with eight races still yet to be called by CNN.

What’s unclear is who will run against Pelosi on the Democratic side. Ohio Reps. Marcia Fudge and Tim Ryan both have told CNN they are not ruling out a bid.

Drew Hammill, Pelosi’s spokesman, projected confidence that she would get the votes.

“Leader Pelosi is very confident in her support among Members and Members-elect,” Hammill said.

A senior Democratic aide said Pelosi would not be deterred.

“Members on the ‘list’ are all to the right of Pelosi,” the aide emailed. “Pelosi will take this to the floor in January, so she will be calling their bluff.”

CNN confirmed on Thursday through multiple aides and members which Democrats signed the letter pledging not to vote for Pelosi. The signatures include 12 incumbents, four incoming freshmen and Ben McAdams, who ran against Mia Love and whose race has not yet been projected by CNN.

  • Anthony Brindisi of New York
  • McAdams of Utah
  • Rep. Jim Cooper of Tennessee
  • Joe Cunningham of South Carolina
  • Rep. Bill Foster of Illinois
  • Max Rose of New York
  • Jeff Van Drew of New Jersey
  • Rep. Filemon Vela Jr. of Texas
  • Rep. Linda Sanchez of California
  • Fudge of Ohio
  • Rep. Brian Higgins of New York
  • Rep. Seth Moulton of Massachusetts
  • Rep. Stephen Lynch of Massachusetts
  • Rep. Kathleen Rice of New York
  • Rep. Ed Perlmutter of Colorado
  • Rep. Kurt Schrader of Oregon
  • Rep. Tim Ryan of Ohio

This story has been updated to include additional reporting on who signed the letter.

CNN’s Elizabeth Landers contributed to this report.