Representative Hakeem Jeffries of New York, the Democratic House leader, on Monday accused Gov. Greg Abbott of Texas of deliberately delaying a special election in a solidly Democratic district in Houston in order to cushion the House Republicans’ slim majority.
Mr. Jeffries said in an interview that Mr. Abbott had been “feverishly working to deny representation to the people of Houston” and to help Republicans in the House pass a budget favored by President Trump that is expected to include cuts to Medicaid and other services.
“House Republicans are running scared legislatively and politically, which is why Gov. Greg Abbott is slow-walking the special election to replace Sylvester Turner,” Mr. Jeffries said. “They are rigging the system.”
Republicans hold a slim 218-to-213 majority over Democrats, but two open House seats in Florida are likely to be filled by Republicans after a special election on Tuesday. Mr. Trump also pulled his nomination of Representative Elise Stefanik to the United Nations, fearing that a vacant seat in her New York district could be won by a Democrat.
Two House Democrats, Representatives Sylvester Turner of Texas and Raúl M. Grijalva of Arizona, died in the early months of this Congress.
The Texas governor had until the end of last week to call a special election in time for the vote in Mr. Turner’s 18th Congressional District to be held on May 3, the next regularly scheduled Election Day in the state.
Instead, Mr. Abbott, a Republican, did not act, and has not said when he will call the election to replace Mr. Turner, who died on March 5 after two months in office.
By doing so, Mr. Abbott has helped House Republicans. Democrats in New York, with Mr. Jeffries’s encouragement, had threatened a similar gambit for Ms. Stefanik’s seat before Mr. Trump left her in it. Meanwhile, Arizona’s Democratic governor, Katie Hobbs, has decided to leave a heavily Democratic House seat in Tucson, Ariz., vacant until after a special election in September.
Mr. Abbott is not explicitly required to call a special election by law, though he has usually done so within days or weeks after similar congressional vacancies. He has the power to schedule an emergency special election, or he could wait and call it for the next regularly scheduled election, in November.
Or he could try not to call it at all and hold the seat open until 2026.
At a news conference in Houston on Monday, one of the Democratic candidates for the open seat, Christian Menefee, stood near a poster highlighting how swiftly Mr. Abbott had called for other special elections. He called on the governor to schedule an election for June.
“Governor Abbott has acted on this responsibility before,” said Mr. Menefee, the Harris County attorney. “The 18th Congressional District is not a political toy,” he added, addressing the governor. “Your silence is suppression.”
Mr. Menefee said that if the governor tried not to call a special election at all, he would file suit against him.
The 18th Congressional District includes some of Houston’s oldest Black communities as well as its downtown.
“This moment requires us to place people over politics,” said Amanda Edwards, a former City Council member and another Democratic candidate for Mr. Turner’s seat. “Failure to do so will leave the nearly 800,000 community members unrepresented.”
Some political observers said that while Mr. Abbott could have called the election for May, doing so would have created potential logistical challenges for the county given the relatively tight time frame. And Mr. Abbott had little incentive to rush.
“Not holding the election until November (or perhaps in the summer) will provide concrete legislative benefits to Speaker Johnson and President Trump,” Mark P. Jones, a professor of political science at Rice University, wrote in an email. Those hurt are House Democrats like Mr. Jeffries, he said, and voters in the district who have not supported the governor.
Mr. Jones added that the governor could wait until November and still be on solid legal ground.
A spokesman for Mr. Abbott declined to address the Democrats’ criticisms and to say whether the governor had spoken with House Republicans about the Houston seat.
“An announcement on a special election will be made at a later date,” the spokesman, Andrew Mahaleris, said in a statement.
J. David Goodman is the Houston bureau chief for The Times, reporting on Texas and Oklahoma. More about J. David Goodman
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