Surprise results in state house speaker elections in Pennsylvania and Ohio could provide a model for how the House of Representatives may move past the deadlock over its speaker election.

In Pennsylvania, state lawmakers elected Mark Rozzi as speaker of the House. Mr. Rozzi, a Democrat, said he wouldn’t caucus with either party, though he did not clarify whether he would formally leave the Democratic Party.

Lawmakers in the Keystone State were forced to cut a deal because — just as on Capitol Hill — Republicans currently enjoy only a thin margin that is likely to be lost when the results come in from three special elections in Democratic districts later this month.

Republicans had initially hoped to use their majority to elect a speaker of their own and then push the special elections back until later this year, but GOP representatives were unable to consolidate around a single candidate.

Ultimately, 16 Republicans defected from the Republican candidate, Representative Carl Walker Metzgar, joining all of the Democrats to elect Mr. Rozzi as speaker. Mr. Rozzi was nominated by Representative Jim Gregory, a Republican.

Although most Republicans did not vote for Mr. Rozzi to be speaker, the House GOP leadership in the state acknowledged that it had few other options. “Reflecting the realities of an evenly divided chamber, it is imperative we have a truly independent voice to conduct House business and manage the House floor,” the Pennsylvania House Republican leadership said in a statement.

Just to the south, the Buckeye State also had a surprise speaker election at its state house. Representative Jason Stephens, a moderate Republican, snatched victory from the hands of Representative Derek Merrin, who was elected in an internal party election.

Mr. Stephens ran to snub the right wing of the GOP, which was backing Mr. Merrin, and halt far-right policymaking in Ohio by cutting a deal with the Democratic conference. “I pledge to respect and to work with each and every one of you,” Mr. Stephens said in his acceptance speech Tuesday.

The Democrats, eager to find a speaker they felt they could work with, backed Mr. Stephens in his bid for the speakership with no defectors.

“They needed our votes and we took the opportunity to make sure that we were going to be working with the speaker who we felt at the end of the day would work with us on the issues we could agree on,” the state Democratic minority leader​, Allison Russo, said.

Both Pennsylvania and Ohio have successfully escaped the deadlock that has ensnared the House of Representatives and, if history is a lesson, could go on much longer.

The worst-case scenario is a repeat of the historic speaker election of 1923, which went to nine ballots before Speaker Frederick Gillett was elected.

In 1923, it was eventually the support of President Coolidge that tipped the scales in favor of Gillett. In 2023, presidential influence doesn’t seem to have as much sway.

President Trump re-endorsed Representative Kevin McCarthy for the role of speaker in a Truth Social post Wednesday morning, after talking with insiders last night.

“Some really good conversations took place last night, and it’s now time for all of our GREAT Republican House Members to VOTE FOR KEVIN, CLOSE THE DEAL, TAKE THE VICTORY, and WATCH CRAZY NANCY PELOSI FLY BACK HOME TO A VERY BROKEN CALIFORNIA,” Mr. Trump wrote.

President Biden, aligned with the Democratic nominee for speaker, Representative Hakeem Jefferies, has resigned himself to the role of spectator.

“With regards to the fight over the speaker… that’s not my problem,” the president told reporters before departing for a photo opportunity in Kentucky with Senator McConnell, now the longest-serving Senate party leader in U.S. history. “I just think it’s a little embarrassing.”

There is one name that has been floated as a compromise candidate in the mold of the deals struck in Pennsylvania and Ohio — Representative Fred Upton of Michigan.

Mr. Upton told the Detroit News that he is intrigued by the offer, but says “I would need Democrats,” who are united behind Mr. Jefferies. Mr. Upton, however, has endorsed the idea of a power-sharing agreement.

“That’s the only way we’re going to get anything done for the next two years,” he said. “The Republican majority is too slim, and we’re too divided, to get significant legislation passed.”

Mr. Upton, a member of the the Problem Solvers Caucus who retired in 2022, was one of 10 Republicans that voted to impeach Mr. Trump the second time and joined Democrats to pass the CHIPS Act.

In the fifth and latest round of voting, the House again failed to elect a speaker, with Mr. McCarthy shedding one supporter since Tuesday, Representative Victoria Spartz, who decided to vote “present” instead of supporting a candidate.

The latest vote total stands at 212 votes for Mr. Jefferies, 201 votes for Mr. McCarthy, 20 votes for Representative Byron Donalds, and one “present” vote.