National Republican Senatorial Committee Chairman John Cornyn (Texas) refused to predict that Republicans would secure a majority in the Senate on “Fox News Sunday.”

“We’re going to fight for every seat we can possibly get,” he said. “It’s a theoretical pathway there, but I’m not predicting we’re going to get back to the majority. It may be a two-cycle process.”

Cornyn, who appeared alongside Sen. Claire McCaskill (D-Mo.), did predict several long-shot GOP wins in the upcoming midterm elections, including a victory for Republican Sharron Angle over Senate Majority Leader Harry Reid (D) in Nevada.

“I certainly think that is a tough race,” McCaskill said. “When you are the leader of the party in power during very tough economic times, you pay a price for that.” Still, McCaskill said she was hoping Reid could overcome the tea party favorite.

Cornyn also said he believes that Republican Linda McMahon will upset Connecticut Attorney General Richard Blumenthal (D) in the Senate race in that state.

McCaskill identified long-shot Democratic victories, including in her home state of Missouri, where she believes Democrat Robin Carnahan could still pull ahead of Rep. Roy Blunt (R) for the open Senate seat.

Additionally, McCaskill said she predicts that in Kentucky, Democrat Jack Conway, the state’s attorney general, will overtake Republican Rand Paul.