"We're facing some difficult times and there's a lot of enthusiasm for the policies that Secretary Zinke and the president have been talking about with regard to our economy. But the message was pretty clear," Sullivan added.

Murkowski on Tuesday joined senate Democrats in voting against a procedural measure to begin debate on healthcare legislation.

Murkowski also voted against a key proposal repealing and replacing ObamaCare later in the day.

Trump on Wednesday targeted Murkowski after her votes.

"Senator @lisamurkowski of the Great State of Alaska really let the Republicans, and our country, down yesterday," Trump tweeted. "Too bad!"

Murkowski said Wednesday she is in her position to govern and legislate. She said she didn't think every day should be about "campaigning" and "winning elections."