Senate Republican leader Mitch McConnell of Kentucky scoffed at claims that a primary in his home state is a referendum on his own popularity -- just one of the closely watched themes in Tuesday's contests.
"I don't know who is going to win," McConnell said on NBC's "Meet the Press" on Sunday. "I expect Kentucky is going to be in a pretty Republican mood this fall."
McConnell endorsed Secretary of State Trey Grayson over Rand Paul, a favorite of the Tea Party movement and son of Republican Rep. Ron Paul of Texas, for an open Senate seat. Polls show Paul with a clear lead over McConnell's pick.
In addition to testing the appeal of the minority leader in his home state in an election year marked by anti-incumbent voter sentiment, the Kentucky Republican primary also is shaping up as a grudge match between the insurgent Tea Party movement and establishment Republicans.
The Tuesday primary races in Kentucky, Arkansas and Pennsylvania dominated Sunday public affairs programming, along with a preview of the coming battle over Solicitor General Elena Kagan's nomination to the Supreme Court.
Sen. Arlen Specter, a Pennsylvania Democrat who switched parties last year and faces a tough primary race for the seat he's held for 30 years, told CNN's "State of the Union" that he always voted "in an independent way," regardless of party affiliation.
Rep. Joe Sestak, a former Navy admiral challenging Specter for his seat, predicted a win on Tuesday despite latest polls showing the race a tossup. Sestak has been hitting Specter hard on his party switch and ties to former President George W. Bush.
This week, Vice President Biden is scheduled to campaign for Specter, who supported President Obama's stimulus package and has won strong backing from the White House, which is unusual in a contested primary.
In Arkansas, Democratic Sen. Blanche Lincoln is leading primary challenger Bill Halter, the state's lieutenant governor.
On ABC's "This Week," Sen. Jeff Sessions, an Alabama Republican and member of the Senate Judiciary Committee, said Kagan's testimony could prove critical to her confirmation prospects.
"I think we'll be looking at her testimony, because she has so little other record," Sessions said. "This is going to be a big deal. It's so important how she testifies."
Appearing on the same show, Democratic Sen. Patrick Leahy of Vermont, chairman of the Judiciary Committee, said Republican concern over Kagan's role in allowing military recruiters on campus when she was dean of Harvard Law School is a nonstarter.
"This is like in Shakespeare, sound and fury signifying nothing," Leahy said. "This recruiting thing -- if somebody wants to go in the military, they usually find a recruiter. I mean, I don't think there was a recruiting station on the campus when my youngest son went and joined the Marine Corps."
On "Fox News Sunday," meanwhile, former first lady Laura Bush threw her support behind Kagan.
"I think it's great," Bush said. "I'm really glad that there will be three [women] if she's confirmed. I like to have women on the Supreme Court."