Progressive Democrats irate over the prospect of the Supreme Court overturning Roe v. Wade are directing some of that ire at one of their own — Congressman Henry Cuellar, the last House Democrat who openly opposes abortion.

Progressives have tarred Mr. Cuellar as “anti-choice” and demanded that the party leadership abandon the South Texan ahead of a closely contested runoff on May 24 against the progressive favorite, Jessica Cisneros.

The more moderate wing of the party has held fast so far. The House whip, Jim Clyburn, the South Carolina kingmaker, appeared at a San Antonio rally with Mr. Clyburn on Wednesday.

At the rally, Mr. Clyburn reiterated his support for Mr. Cuellar and said having him among the Democratic ranks is knowing the party has somebody “who can respect other people’s opinions and do it in such a way that you can get the 218 votes you need.”

The infighting comes at a perilous time for the Texas Democrats. Mr. Cuellar’s 28th district, covering much of the Rio Grande Valley along the U.S.-Mexico border, has been solidly Democrat for decades. In 2020, however, the region turned purple. The 28th is now the only match in Texas considered a toss-up.

Republicans believe the 28th is primed to be picked off from the Democrats in November, along with two other South Texas districts, and they have a former staffer for Senator Cruz, Cassy Garcia, waiting in the wings to challenge Mr. Cuellar in November.

The progressive feud with Mr. Cuellar is not new, but reached a fever pitch following the leak Monday of a draft Supreme Court opinion overturning Roe v. Wade. Representative Alexandria Ocasio-Cortez said it was time to hold “GOP & Dem obstructionists” accountable and tweeted a link to Ms. Cisneros’s fundraising website.

Her comments were followed by tweets suggesting more of the same from the likes of the Working Families Party, People for Bernie, an Obama administration alum, Julian Castro, and actress Susan Sarandon. 

“Democratic leadership is supporting an anti-choice candidate in Texas right now,” Ms. Sarandon tweeted Wednesday, in all-caps and with sirens for effect.

Senator Warren of Massachusetts appeared at a fundraiser for Ms. Cisneros Tuesday night, after which the candidate weighed in herself. “At every turn, my Congressman has stood in opposition to the Democratic party agenda, from being anti-union to being anti-choice,” Ms. Cisneros said in a statement.

Mr. Cuellar’s moderate leanings have served him well during his 17 years in office. What painted a progressive target on his back was his refusal to sign off on the Women’s Health Protection Act, which would have codified abortion rights in federal law. It passed the House of Representatives in September in response to Texas’s strict new anti-abortion measures. The measure died in the Senate.

Mr. Cuellar was the only Democrat in the House who against the measure. 

At the time, Mr. Cuellar told the Laredo Morning Times that his vote was a “matter of conscience.” In a statement released Tuesday, the congressman reiterated his opposition to abortion as a Catholic but criticized the potential Supreme Court ruling, if it emerges as is, as likely to “further divide the country in these already divisive times.”

In addition to being supported by Senators Warren and Sanders, Ms. Cisneros — a 28-year-old immigration lawyer who once interned in Mr. Cuellar’s office — has been endorsed by prominent abortion-rights groups such as NARAL Pro-Choice America and Emily’s List.

An additional drag on Mr. Cuellar’s campaign is an FBI raid on his Laredo, Texas, home and campaign offices in January. The Justice Department has remained mum about the investigation, but it reportedly involves ties between U.S. businesses and Azerbaijan, to which the congressman traveled with his wife in 2013. His attorney told Fox News that Mr. Cuellar is not a target of the investigation.

Mr. Cuellar narrowly edged out Ms. Cisneros in the March 2 primary, winning 48.6 percent of the vote to Ms. Cisneros’s 46.7 percent, but because neither received a majority, they face each other again in a runoff later this month. When the two faced each other in the 2020 primary, Mr. Cisneros squeaked out a win by 2,700 votes.

President Biden prevailed over President Trump in the district in 2020 by slightly more than four percentage points. Four years earlier, Senator Clinton beat Mr. Trump by nearly 20 percentage points.