In Showdown Over G.O.P. Control in Texas, the Race for House Speaker’s Seat Heads to a Runoff

The Texas House speaker, Dade Phelan, and a local Republican activist backed by former President Donald J. Trump will compete in a runoff in May after neither received enough votes to win on Election Day, according to The Associated Press.

The contest was part of a bruising and bitter Republican primary across Texas in which dozens of incumbents faced well-funded opposition, either from supporters of Attorney General Ken Paxton, who had vowed revenge for his impeachment by the Texas House last year, or from Gov. Greg Abbott, who sought to oust opponents of his plan for school vouchers.

It remained unclear on Tuesday how many of the embattled incumbents, mostly in the Texas House, would survive or would have to continue fighting until the runoff on May 28. Candidates, consultants and voters said they had never before seen a Republican primary as hard-fought, expensive and widespread across so many districts.

But Mr. Phelan’s failure to secure his seat on Tuesday indicated that those fights over the future direction of the Republican Party would continue roiling the state.

Mr. Abbott did not make an endorsement in Mr. Phelan’s race. But he aggressively campaigned against state representatives who opposed his proposal to give public money to parents to spend on private schools. His campaign received a $6 million contribution from a Pennsylvania school voucher supporter, and it spent more than that amount on House races.

His goal was to shift the balance of power in the Texas House so that a private school voucher measure would pass in the next legislative session. It was not clear on Tuesday if that effort had paid off.

Mr. Paxton also aggressively targeted three Republican judges who serve on the Court of Criminal Appeals, hoping to remake the state’s highest criminal court. The attorney general criticized the judges as “Republicans in name only” for their part in an 8-to-1 ruling by the all-Republican court barring Mr. Paxton from unilaterally prosecuting criminal cases of voter fraud without going through local district attorneys.

All three judges were trailing on Tuesday night — two of them by wide margins.

Mr. Phelan had been a key focus for Mr. Paxton, who campaigned heavily for his opponent David Covey, a little-known county party leader, and helped to secure a pivotal endorsement for Mr. Covey from Mr. Trump. Lt. Gov. Dan Patrick, the conservative leader of the State Senate, also cut sharply critical advertisements against Mr. Phelan.

Mr. Phelan had not faced an opponent of either party in a decade in his Southeast Texas district.

“Why am I being opposed now?” he said in an interview outside an early voting center last month. “Because I took on corruption within my party, and I said: ‘I am not going to stand for it. Not today, not tomorrow, not ever.’”

Mr. Covey received backing from Texans United for a Conservative Majority, a group whose two primary funders are Tim Dunn and Farris Wilks, religious conservatives and West Texas oil and gas billionaires who together contributed more than $4.5 million to this year’s races, mostly to support challengers.

Both men have backed Mr. Patrick and Mr. Paxton in the past and have tried for years to push Texas politics to the right through a different groups and political action committees.