The unidentified woman, captured by a local television crew while speaking from the podium Saturday, told the crowd that Murray should suffer the same fate as the character Jake in the western "Lonesome Dove."
"What happened to Jake when he ran with the wrong crowd?" the woman asked. "He got hung. And that's what I want to do with Patty Murray."
The crowd erupted in laughter at the comment. Organizers estimated that approximately 500 people attended the weekend meeting of the Lewis & Clark Tea Party Patriots.
Television station KLEW of Lewiston, Idaho, which recorded the comment, did not get the woman's name.
Event organizer Dianne Capps said the woman's remark was not made in malice. The speaker was on stage briefly to introduce the band, and organizers did not know who she was, Capps said.
Another organizer, Doug Schurman, added that anyone was welcome to speak at the gathering.
Murray's campaign manager, Carol Albert, said Thursday the woman's comments were not productive.
Albert said Murray shares the frustrations of many people at the slow pace of the economy and partisan gridlock in Washington, D.C.
"But positions like that taken by the Tea Party spokesperson have never solved a problem," Albert said in a statement. "What people want right now is for people to come together to find solutions, not more rhetoric that drives us apart."
Murray, a liberal senator, is seeking a fourth term this year. Among the Republicans who have announced plans to challenge her are two small-government conservatives: Clint Didier, a farmer who formerly played football for the Washington Redskins, and state Sen. Don Benton.
Didier has participated at previous tea party events, but it was unclear if he attended Saturday's gathering. His spokesman did not immediately return a call Thursday.
The meeting also featured signs that read "Geld Obama" and "B.O. Stinks."
The tea party movement has brought together a broad coalition of retirees, stay-at-home moms, small-business owners, corporate executives and others who are frustrated about the direction of the nation and want to take back control.
The coalition is decidedly conservative and libertarian, and has spoken out harshly against President Barack Obama and the Democratic-controlled Congress. They have also been critical of Republicans.