[cnn-photo-caption image= http://i2.cdn.turner.com/cnn/2010/images/04/15/art.tthompson0415.gi.jpg caption ="Former Wisconsin Gov. Tommy Thompson has decided not to run for Senator."](CNN) - Former Wisconsin Gov. Tommy Thompson has decided against mounting a Senate bid, dealing a blow to Republicans who viewed him as the party's best chance to topple incumbent Democrat Russ Feingold.
"My family didn't want me to run," Thompson told the Milwaukee Journal Sentinel Thursday about his decision not run. The onetime presidential candidate announced his decision at a Tea Party rally outside the Wisconsin State Capitol.
"It's time for new voices and new faces," Thompson told the crowd, according to local television station WBAY.
Thompson, who was governor of Wisconsin for 14 years and served as health and human services secretary under former President George W. Bush, remains popular in his home state. Recent polls showed that Thompson was running neck and neck with Feingold in a hypothetical matchup.
Thompson's decision leaves the race for the GOP Senate nomination to businessman Terrence Wall and former State Commerce Secretary Dick Leinenkugel - neither of whom have high name recognition throughout the state.
Feingold, who is seeking his fourth term as senator, is sitting on $4 million in campaign cash as he awaits an opponent, according to his campaign.
UPDATE 4:48 p.m.:
The Feingold campaign put out a statement Thursday afternoon with Sen. Feingold's reaction:
"I'm disappointed that Secretary Thompson decided not to get in the ring. I'm sure there will now be talk about other candidates getting in this race, but it's my hope that the election can now be focused where it should be – on the issues important to the people of Wisconsin and who will be an independent voice for them in Washington, working hard to move our state forward."