WASHINGTON—Sen. John Cornyn, who is spearheading the Republicans' campaign to take back the Senate, is on a roll. The GOP snatched a seat in Massachusetts and polls favor Republicans in many key states.

But the genial Texas lawyer is facing an unusual challenge—from one of his own colleagues. Firebrand conservative Sen. Jim DeMint of South Carolina, breaking with the Senate's tradition of deference, is endorsing and funding conservative candidates to challenge the party establishment's picks. Just last week, he backed a conservative...