The White House is talking to members of Congress about potential changes to the D.C. statehood bill that could reduce opposition in the Senate, White House press secretary Jen Psaki said Thursday.

The Biden administration’s involvement in negotiating the bill’s future follows its strong endorsement of D.C. statehood last month, just before the Washington, D.C. Admission Act was approved by the House on a strict party-line vote.

The bill’s odds are much steeper in the evenly divided Senate, with Republicans dismissing D.C. statehood as an unconstitutional Democratic power grab.

“Our view is that admitting D.C. as a state is well within Congress’s power and that the arguments to the contrary are faulty,” Psaki said during a White House news briefing. “But we also think there are ways to allay the concerns that have been raised. And that’s why we’re working with Congress to make the bill as strong as possible.”

Psaki was asked about the issue after the New York Times reported that White House lawyers are pushing a potential change to the bill involving the 23rd Amendment. Republicans have frequently pointed to that amendment as an insurmountable hurdle for D.C. statehood. The amendment, ratified in 1961, gave D.C. residents a say in presidential elections by granting the federal district three electoral votes, awarded on the basis of the popular vote by city residents.

Under the statehood bill, the federal district — the seat of government — would shrink to a two-mile enclave including key federal buildings and monuments. The rest of the city would become the state of Washington, Douglass Commonwealth.

Like any new state, the commonwealth would get electoral votes equal to its number of senators and House representatives three in all, in this case. The question that has lingered is what would happen to the three electoral votes that the 23rd Amendment grants to the federal district? The only residents living there would presumably be those at 1600 Pennsylvania Avenue — and Democrats and Republicans agree that the president’s family should not control three electoral votes.

The statehood legislation, sponsored by Del. Eleanor Holmes Norton (D-D.C.) and Sen. Thomas R. Carper (D-Del.), calls on Congress to expeditiously repeal the 23rd Amendment as soon as D.C. becomes a state. The amendment gives Congress the power to decide how the federal district’s electors are appointed and to pass legislation enforcing the amendment; the statehood bill also seeks to repeal that legislation, effectively nullifying the amendment even before it is repealed.

The Times reported that White House lawyers are pushing to change that provision, so the federal enclave would keep its electoral votes, which would be awarded to the winner of the national popular vote. Columbia Law School professors Jessica Bulman-Pozen and Olatunde Johnson proposed the same thing last year.

Bulman-Pozen said she didn’t see any legal issues with the current bill but believed it was more consistent with the text of the 23rd Amendment to appoint electors in the federal district than for Congress not to appoint any.

“I think it’s plausible and consistent with the democratic spirit of the 23rd Amendment . . . to make that [shrunken federal] district responsible for representing the people of the United States,” she said.

Norton indicated she was open to changes relating to the 23rd Amendment in her bill, saying in a statement: “There are a number of different ways to deal with the electoral votes in the reduced federal district and any of them would be satisfactory.”

A spokesman for Carper said the senator is having active conversations with the Biden administration regarding efforts to pass the bill. He did not give details.

Forty-six of the 50 senators in the Democratic caucus have backed the statehood bill, with the addition of Sen. Jeanne Shaheen (D-N.H.) this week. An aide on the Senate Committee on Homeland Security and Governmental Affairs said Chairman Gary Peters (D-Mich.) plans to hold a hearing on the bill in the next few months.

Sen. Joe Manchin III (D.-W.Va.), one of the four Democratic senators who have not supported the bill, said last month that he viewed the 23rd Amendment as a chief obstacle. But he also said he believes D.C. statehood can only be achieved through a constitutional amendment, not through legislation.

Rep. Jamie B. Raskin (D-Md.), a former constitutional law professor and statehood supporter, disagrees. He called the 23rd Amendment debate a “made-up issue, a sideshow” and argued that if D.C. becomes a state, the amendment should be viewed as irrelevant, just as the fugitive-slave clause in the Constitution became irrelevant with the abolition of slavery.

“They think somehow it would be unconstitutional for the 23rd Amendment to be sitting out there for a few months or a year before its repeal is accomplished,” Raskin said. “Why? . . . No one’s rights are violated, and no constitutional purpose is frustrated. The purpose of the 23rd Amendment was to give people the right to participate in presidential elections. That purpose is completely vindicated by statehood.”

Raskin said he believed the statehood bill was fine as is but added that if any change had the potential to draw in more supporters, it was worth a shot: “I think it makes all sense in the world to explore different options.”

seung-min.kim@washpost.com

Matt Viser contributed to this report.