Barbour spoke at a news conference Wednesday as the Republican Governors Association began a conference in Austin, Texas, The Washington Post reported. Barbour, a former chairman of the Republican National Committee, is the current head of the RGA.
When Chris Christie is inaugurated in New Jersey in January and Robert McConnell in Virginia, 24 states will have Republican governors. Next year, there will be gubernatorial elections in 37 states.
"Our goal for next year is to get appreciably above a majority," Barbour said.
The governors have been focusing on policy issues, including the Senate healthcare proposal released this week by Majority Leader Harry Reid, D-Nev. Most of those at the meeting said the plan would drive costs up in the states.
The emphasis on policy has its political side -- demonstrating that Republicans have their own vision of the country's future.
"Republican governors are making a difference and we are leading the comeback," Barbour said.