The longtime senator has had a rough month. He's dogged by residency issues that have drawn attention to the fact that he lives in Washington, D.C.'s suburbs and hasn't owned a home in Indiana for decades. Conservative national groups have also rallied to Mourdock — his latest endorsement came from the National Rifle Association.

Lugar has a major cash advantage, and support from popular Indiana Gov. Mitch Daniels (R) could help his campaign. But numbers like these less than two months before the primary should concern his reelection bid.

The poll of 500 likely Republican primary voters was conducted March 12-15 by the Global Strategy Group.