A renewed push by Nebraska Republicans to move to a “winner-take-all” system in presidential elections has raised the prospect that the 2024 contest could end in an electoral college tie — with the House of Representatives deciding the winner.

Nebraska and Maine are the only states that divide their electoral votes according to the presidential winners of congressional districts. In 2020, Joseph R. Biden Jr. won the eastern district around Omaha and its one vote. On Tuesday, Gov. Jim Pillen of Nebraska, a Republican, threw his support behind a G.O.P.-led bill languishing in the state’s unicameral legislature that would end the practice.

“It would bring Nebraska in line with 48 of our fellow states, better reflect the founders’ intent, and ensure our state speaks with one unified voice in presidential elections,” Mr. Pillen wrote in a statement.

The resurrection of the state bill was sparked this week by Charlie Kirk, the chief executive of Turning Point USA, a pro-Trump conservative advocacy group, who pressed the state legislature to move forward on social media.

Former President Donald J. Trump quickly endorsed the governor’s “very smart letter” on his social media site.

And for good reason. If Mr. Biden were to hold Wisconsin, Michigan and Pennsylvania, but lose Georgia, Arizona, Nevada and the one Nebraska vote he took in 2020, the electoral college would be deadlocked at 269 votes each. The House would then decide the victor, not by total votes but by the votes of each state delegation. That would almost certainly give the election to Mr. Trump.

But that Sun-Belt-sweep-plus-one scenario still might be out of reach. Democrats in the legislature expressed confidence on Tuesday that they could filibuster the measure, and the state legislative session is set to end on April 18.

Conversely, Maine, where Democrats hold the governor’s office and a majority in the legislature, could change its system to take back the electoral vote that Mr. Trump won in 2020. Mr. Biden won Maine by nine percentage points, but Mr. Trump took a vote in the electoral college by winning the state’s rural second district.