SPRINGFIELD, Mo. -- U.S. Sen. Claire McCaskill says Republicans have already started courting her and other moderate Democrats to be swing votes on major legislation in the next Congress.

The Missouri senator said the new Republican majority seeks Democrats' help on major initiatives such as transportation legislation and corporate tax reform, the Springfield News-Leader reported. She said U.S. Sen. Rand Paul, R-Kentucky, has already approached her about teaming up.

"They're all being very nice," McCaskill said.

McCaskill previously broke with Democratic Party leadership when she voted against U.S. Sen. Harry Reid of Nevada to be the minority leader. She also wants to approve authorizing the construction of the Keystone XL oil pipeline.

Most legislation in the Senate requires 60 votes to avoid the threat of a filibuster and the GOP will hold 54 votes next year. There will be about a dozen moderate Democrats left in the Senate come January, down from about 18 in 2011. The moderate Democrats are informally organized, McCaskill said.

"We're always on the floor and kind of huddling, and we talk to each other and text and email and phone," she said. "I usually hear from one of my moderate colleagues at least on a weekly basis."

Republicans "now have the responsibility to do something more than object," McCaskill said. "They can't do it unless they attract some Democratic votes."

Winning the support of moderate Democrats "will be the way that we can maybe bring compromise together in very effective ways," said Sen. Orrin Hatch, R-Utah. "So I'm counting on some of them."