House Majority Leader Eric Cantor was supposed to cruise to victory in Tuesday's GOP primary over Dave Brat, but the immigration issue almost certainly doomed his hopes for an election, according to The Associated Press.

Senator Lindsey Graham of South Carolina and House Majority Leader Eric Cantor of Virginia are favored to fend off Tea Party challengers in Republican primaries on Tuesday when voters in five states pick candidates for the Nov. 4 midterm elections, the AP reported.

The Graham and Cantor showdowns are the latest in a series of primary clashes between the conservative Tea Party movement and the Republican establishment this year, the AP reported. The Tea Party is seeking its first high-profile win after a string of losses.

It came close last week in Mississippi, when Tea Party favorite Chris McDaniel fell just short of the majority needed for an outright win but forced six-term U.S. Senator Thad Cochran into a June 24 run-off, according to the AP.

Graham, a prominent foreign policy hawk who has angered some conservatives for his willingness to work with Democrats, hopes to avoid a run-off with the second-place finisher by capturing 50 percent of the vote in his crowded South Carolina primary, the AP reported.

Graham has moved aggressively to beat back a challenge from the right, touting his conservative credentials and spending more than $8.5 million since January 2013 in preparation for a primary race, according to fundraising figures compiled by the Center for Responsive Politics, according to the AP.

A Clemson University poll last week showed Graham within reach of victory with about 49 percent of the likely primary vote and one-third of voters still undecided, the AP reported.

The South Carolina field of challengers to Graham, a two-term U.S. senator, includes a minister, two lawyers and a state senator who gave away a handgun at a campaign event, according to the AP.

Cantor, the No. 2 Republican in the U.S. House of Representatives, also has been accused of not being conservative enough by his Tea Party challenger, David Brat, an economics professor at Randolph-Macon College, the AP reported.

Like Graham, Cantor has responded aggressively and recently sent voters in his central Virginia district a mailer boasting of his efforts to kill House immigration legislation that would have offered what he called amnesty to undocumented workers, according to the AP.

Cantor spent $5 million during this election cycle, according to the Center for Responsive Politics, the AP reported. Brat spent about $122,000 during the same period.