Gay GOP group GOProud on Wednesday endorsed former Wisconsin Governor Tommy Thompson for the U.S. Senate over Rep. Tammy Baldwin.

The 50-year-old Baldwin would become the first openly gay U.S. senator if she captures the seat being vacated by Wisconsin Senator Herb Kohl.

Last week, voters decided on Thompson as her Republican rival.

“Tommy Thompson is a common-sense conservative who will focus on creating jobs and growing the economy for all Wisconsin,” Jimmy LaSalvia, executive director of GOProud, said in a statement. “Governor Thompson's experience and leadership uniquely qualify him to serve in the U.S. Senate.”

The group noted that Thompson opposes a federal constitutional amendment banning gay marriage. But the GOP candidate remains opposed to legalizing gay nuptials and has previously voiced support for the Defense of Marriage Act (DOMA).

Thompson's record on gay rights also includes him saying in 2008 that he believes businesses should have the right to fire gay employees. The next day during an appearance on HBO's Real Time with Bill Maher, he profusely denied he believes in discrimination in the workplace based on sexual orientation, explaining that he was not feeling well and did not answer the question correctly.

GOProud's Christopher R. Barron knocked Baldwin as being a “rubber stamp for the disastrous big government policies of the far left.”

(Related: Tammy Baldwin endorsed by lesbian super PAC.)