Sen. Lisa Murkowski (R-Alaska) said Wednesday that Alaska voters won't be swayed by the efforts of Sen. Jim DeMint (R-S.C.), who is funding a campaign ad that hits Murkowski's stance on abortion.

The 30-second spot, which will start airing in Alaska this week, is paid for by DeMint's Senate Conservatives Fund and assails his GOP Senate colleague for supporting publicly-funded abortions.  

"Jim DeMint knows, as does Joe Miller, that I have always drawn the line on federal funding for abortion," Murkowski said Wednesday in an interview with CNN's John King. 

Emphasizing that DeMint hails from South Carolina, Murkowski predicted Alaska voters will reject the attack and that they won't take kindly to those from outside the state who are trying to influence the race.

"This is our state, this is our race and we will be the ones choosing who will represent us in the Senate," Murkowski said.  

DeMint has been one of Murkowski's most outspoken critics since she announced her decision to run as a write-in candidate after losing the GOP primary to Tea Party favorite Joe Miller.

Last month, he argued that Murkowski be stripped of her top spot on the Energy and Natural Resources Committee, a move the Senate Republican caucus declined to make.

On Wednesday, Murkowski touted her status on the committee, noting on CNN that it puts her in a position to deliver much needed opportunities to her state. 

She also warned that Miller and others are offering "very simplistic solutions" to the nation's economic problems. 

"When you're talking about reducing spending, let's not deceive people into thinking that if you eliminate earmarks, suddenly you won't be operating at a deficit," she said. 

A new CNN/Time poll released Wednesday had Murkowski in a dead heat with Joe Miller at 37 percent a piece. Democrat Scott McAdams polled third with 23 percent.