Updated at 11:15 a.m. ET
Republican Rep. Paul Ryan has decided to stay out of the open 2012 Wisconsin Senate race, leaving the door open for former Wisconsin Gov. Tommy Thompson.
In a statement on his website, Ryan said he could make the biggest difference for the nation and Wisconsin in the House.
"I believe continuing to serve as Chairman of the House Budget Committee allows me to have a greater impact in averting this debt-fueled economic crisis than if I were to run for the United States Senate," he said. "House Republicans have taken bold steps forward in tackling our fiscal and economic challenges - we have led, where others have not."
Attention quickly turned to Ryan last week after Democratic Sen. Herb Kohlthat he is retiring after four terms in the Senate. Wisconsin has proven to be a fiercely competitive political battleground in recent months, and Ryan was considered one of the strongest contenders for the open seat. His profile in the Republican party shot up this year after he took the lead on fiscal issues as chairman of the House Budget Committee, introducing a politically bold 2012 budget proposal.
Thompson, a high-profile Republican in Wisconsin, has told top Republican officials that he intended to run for the Senate should Ryan take his name out of the running, a GOP strategist tells CBS News. In addition to governor, Thompson served as President George W. Bush's Health and Human Services Secretary.
Thompson may now be considered the top Republican candidate for the seat, but there are several other potential GOP contenders, the Milwaukee Journal Sentinel reports, including state Attorney General J.B. Van Hollen, state lawmakers Jeff and Scott Fitzgerald, former U.S. Rep. Mark Neumann, and former U.S. Rep. Mark Green.
On the Democratic side, potential contenders include Milwaukee Mayor Tom Barrett and U.S. Reps. Ron Kind and Tammy Baldwin. The liberal group Democracy for America is actively petitioning for former Sen. Russ Feingold to enter the race, calling him a "progressive champion."
Feingold's recent electoral defeat in Wisconsin, however, proves how challenging the race could be. In spite of his relatively high profile in the Senate and strong support from progressive voters, Feingold lost his 2010 re-election bid. Republicans last year carried several races in Wisconsin, winning the governor's office, both houses of the state legislature, and two congressional seats, along with Feingold's former Senate seat.
But as the Wisconsin GOP attempted to institute its agenda this year, Republican lawmakers faced afrom voters upset over some policy changes, chief among them new limits on labor union rights.