No,All that matters for electing the speaker is that a majority of votes is won by a candidate. It doesn't matter what party the voters belong to in determining the winner.
In order to get elected to the position of speaker of the house a candidate needs a majority of the votes cast. When voting members have the option of voting for a candidate or voting present which each vote as present reducing the amount of votes needed to win.
How many votes are needed to win the House speaker election?
It is possible to win the speakership without hitting 217 in this Congress, but in order to do so, a candidate would have to coax some of those in opposition to change their votes from "no" to "present." Measures are passed in the House with a majority of those who cast a vote.
For instance, McCarthy won the speakership in January on a vote of 216-212, convincing enough of his GOP colleagues who had voted against him to support his bid. The six remaining Republicans who withheld their support for McCarthy up to the final ballot — Reps. Andy Biggs of Arizona, Lauren Boebert of Colorado, Eli Crane of Arizona, Matt Gaetz of Florida, Bob Good of Virginia and Matt Rosendale of Montana — voted present.
Faced with a similarly small majority in 2021, Rep. Nancy Pelosi also won her final speakership with 216 votes. Five Democrats either voted for someone else or voted present, and all of the Republicans voted for McCarthy.