Rather than the winner-take-all process used in most states, the proposed changes would apportion electoral votes by congressional district, as Nebraska and Maine currently do.
Republicans in Virginia, Michigan, Ohio and Pennsylvania came up with the proposals after voters in their states voted for Democrat Barack Obama in the last two presidential elections.
The Virginia state Senate may vote next week on a proposal by Republican state Sen. Charles Carrico to adopt the system currently in place in Nebraska and Maine, where the overall winner gets two extra electoral votes, one for each of the state's U.S. Senate seats.
Virginia state Sen. Donald M. McEachin, a Democrat, called the proposals "sore-loser bills."
The Atlantic reported Friday a spokesman for Virginia Gov. Bob McDonnell, a Republican, said McDonnell "believes Virginia's existing system works just fine as it is."
Virginia state Sen. Ralph Smith, a Republican, said Friday the legislation is a "bad idea" and he will oppose it, The Roanoke Times reported.
"What if all states got to skewering it to their advantage?" Smith said.
Smith is a member of the Senate Privileges and Elections Committee, which is set to hold hearings on the bill next week. If he opposes the bill, it would be difficult for the measure to reach the full Senate, the Times said.
Florida House Speaker Will Weatherford told The Miami Herald he opposes changing the state's Electoral College rules.
"I don't think we need to change the rules of the game," Weatherford said. "I think we need to get better."
Pennsylvania state Senate Majority Leader Dominic Pileggi plans to introduce a bill in February to allocate the state's electoral votes based on the percentage of the popular vote, The Washington Post reported. Obama won Pennsylvania 52 percent to 47 percent in November, taking all 20 of the state's electoral votes. Under Pileggi's proposal, Obama would only have won 12 electoral votes and Republican nominee Mitt Romney would have taken eight.
Mike Tate, chairman of the Democratic Party in Wisconsin, called the bills "an audacious attempt to rig the system."
Republicans "can't appeal to a majority of voters, whether it's here in Wisconsin or Michigan or the rest of the Midwest, so they are undermining a majority of voters," he said.
The Atlantic reported Friday that Jordan Gehrke, a Republican strategist, is working with former Ohio Secretary of State Ken Blackwell to promote similar reforms nationwide.
Gehrke said he and Blackwell have contacted major donors and will send out an email next week asking for financial support from grassroots conservatives to fund an electoral vote reform campaign.