The party can replace Sheila for the upcoming general election. The issue will be if Greg schedules a special election to cover the balance of Sheila's term ending January 3, 2025.
https://www.houstonchronicle.com/politics/houston/article/sheila-jackson-lee-congress-seat-19585390.php
Under state law, the Harris County Democratic Party’s executive committee will have until Aug. 26 to nominate a candidate to run in the Nov. 5 general election.
If the committee does not choose a candidate in time, then the Texas Democratic Party would have two days, or until Aug. 28, to make the choice.
Chad Dunn, a lawyer for the Texas Democratic Party, said state party rules advise that, if possible, there should be at least 10 days from the creation of the vacancy before a meeting is called.
County executive committees will sometimes create an informal filing period, or they may create a survey for candidates to fill out, or they may notice the meeting and ask the candidates to show up in person and make their pitch in front of the committee, Dunn said.
Gov. Greg Abbott has the authority to call a special election to fill the vacancy through the remainder of Jackson Lee’s two-year term, which is up in January. His office did not immediately respond to a request for comment.
Once Abbott calls a special election, the law requires him to schedule it within about two months if it will be held as an emergency election. State law does not set a deadline for Abbott to make the initial announcement.....
The last time a situation like this arose was in 1968 when Democratic U.S. Rep. Joe R. Pool died in July, also about six months before his term ended. In that case, the governor did call a special election for about a month later.
I am betting that Greg will not call a special election
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