Washington residents earned three electoral votes and the right to vote for president in 1961 with the passage of the 23rd Amendment, before securing the right to elect a nonvoting delegate a decade later. Since then, a brief agreement struck with Republicans that would have given that delegate the right to vote fell apart, and the statehood legislation has never survived a floor vote.

The legislation put forward by Ms. Norton would establish the State of Washington, Douglass Commonwealth, and allow for it to have two senators and a voting representative. It would shrink the federal district to the National Mall, the White House, Capitol Hill and some other federal property, and leave the rest of the land for the new state.

Those proposed borders drew scrutiny from Representative Thomas Massie, Republican of Kentucky, who questioned the motivation for putting the Trump International Hotel, which leases federal property on Pennsylvania Avenue, inside the state.

The debate on Thursday broke down along party lines, and it featured many of the same arguments that advocates and District of Columbia officials have grown to anticipate. Opponents argued that granting the overwhelmingly liberal city representation would unfairly guarantee the party votes in the two chambers. They pointed to the District’s history of financial turmoil as evidence that it could not handle being a state. And they said the entire premise of statehood goes against the Constitution.

“This is not what the founding fathers intended,” said Representative Jim Jordan of Ohio, the top Republican on the committee. “They understood, and they carefully crafted the Constitution, so that the seat of the federal government would purposefully and specifically not be within a state.”