The fundraising e-mail is on behalf of Martha Coakley, a Democrat, who is facing Republican Scott Brown in a tight race to replace the late Sen. Ted Kennedy in Massachusetts.
Udall's e-mail reads, in part, "Martha's opponent is receiving millions of dollars in support from far-right tea-baggers across the country, claiming him as one of their own."
The term "tea-bagger," which is also slang for a sex act, has been used by critics of the tea party movement, a conservative push for lower taxes and smaller government.
The movement grew to prominence last year after activists mailed tea bags to lawmakers in reference to the Boston Tea Party and the movement's slogan, "Taxed Enough Already."
The word "tea-bagger" has appeared on signs at anti-tax rallies but movement organizers have long sought to discourage use of the word because of its sexual connotation.
"It's inappropriate," said tea party movement founder Michael Johns. "Especially by someone who should know better."
A campaign representative for Udall, who is not up for re-election until 2014, issued a statement in response to an inquiry by 9NEWS.
"Over the past year, multiple media outlets have used the term as a short-hand reference to tea party activists," the statement read. "That is what was intended by the campaign and nothing more."
A Lexis-Nexis search of television news transcripts indicates the word "tea-bagger" has been used by liberal commentators Rachel Maddow and Keith Olberman on the cable network MSNBC.
A CNN news anchor has apologized after using the term on-air.
After complaints from listeners, National Public Radio has put the word into its "dirty word filter."
"I think it's been disappointing when it's been used by highly-partisan commentators," Johns said. "I find it disappointing and surprising it would be used by a U.S. senator."
Brian Campbell, the organizer of several tea party events in Colorado, found something to like about Udall's reference of the movement.
"It is nice to know that we have accomplished so much near the one year anniversary that Udall will give us mention," Campbell said.
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