Sen. Lisa Murkowski (R-Alaska) said Monday that she couldn't support former Alaska Gov. Sarah Palin for president should she run in 2012, citing Palin's lack of "intellectual curiosity." 

In an interview on the "CBS Evening News" with host Katie Couric Monday, Murkowski said she doesn't think Palin enjoyed governing when she was the state's chief executive and questioned Palin's knowledge of policy. 

"I just do not think she has those leadership qualities, that intellectual curiosity that allows for building good and great policies," Murkowski said on CBS Monday. 

Murkowski has long had an antagonistic relationship with Palin, who backed Tea Party favorite Joe Miller earlier this year in the state's GOP Senate primary. In 2006, Palin defeated Murkowski's father in a primary--former Gov. Frank Murkowski. 

"She was my governor for two years, for just about two years there, and I don't think that she enjoyed governing," said Murkowski. "I don't think she liked to get down into the policy. I want somebody who goes to bed at night and wakes up in the morning thinking about how we're going to deal with our national security issues, how we're going to deal with our economy, how we're going to deal with providing better education." 

Murkowski said currently her relationship with Palin is just about nonexistent, telling Couric, "We just don't really have much in common. I mean, we don't talk to one another." 

Ballots are still being counted in Murkowski's write-in battle against Miller, but the senator's camp appears confident she will come out on top. Elections officials continued the write-in ballot count Monday and Murkowski is still winning close to 90 percent of those votes unchallenged. 

Murkowski received a warm welcome from fellow Senators on the Senate floor Monday and congratulations from National Republican Senate Campaign Chairman John Cornyn (R-Texas). 

Murkowski said she hopes to have some final news on the ballot count by Wednesday.