Republicans in Virginia and a handful of other battleground states are pushing for far-reaching changes to the Electoral College in an attempt to thwart recent success by Democrats.

In the vast majority of states, the presidential candidate who wins receives all of that state’s electoral votes. The proposed changes would instead apportion electoral votes by congressional district, a setup far more favorable to Republicans.

Under such a system in Virginia, President Obama would have claimed four of the state’s 13 electoral votes in the 2012 election, rather than all of them.

Other states considering similar changes include Michigan, Ohio and Pennsylvania, which share a common dynamic with Virginia: They went for Obama in the past two elections but are controlled by Republicans at the state level.

Republican National Committee Chairman Reince Priebus recently voiced support for the effort, saying it is something that “a lot of states that have been consistently blue that are fully controlled red ought to be looking at.”

Sean Spicer, a Priebus spokesman, said Thursday: “For these states, it would make them more competitive, but it’s not our call to tell them how to apportion their votes.”

No state is moving more quickly than Virginia, where state senators are likely to vote on the plan as soon as next week.

If successful, Virginia would become the third state to adopt the congressional district system, after Nebraska and Maine.

The bill’s sponsor, state Sen. Charles Carrico Sr., said his goal is to give smaller communities a bigger voice.

“The last election, constituents were concerned that it didn’t matter what they did, that more densely populated areas were going to outvote them,” he said.

“This is coming to me from not just my Republican constituents,” said Carrico, whose district voted overwhelmingly for Republican Mitt Romney in last year’s presidential election. “I want to be a voice for a region that feels they have no reason to come to the polls.”