"I am honored and humbled and grateful, and I am ready to get to work -- ready to stand with Barack Obama, and ready to fight for Wisconsin's middle class," Baldwin said to raucous cheers at her victory party.
Even during his four-way GOP primary race, Thompson was long considered the frontrunner.
He was a popular governor in the state who later served as President George W Bush's health and human services secretary and enjoyed high name-recognition in the state.
According to the Huffington Post, although Baldwin made history on Tuesday night when she became the first openly gay senator-elect in US history, her sexual orientation was largely a non-issue in the race.
In September, Thompson's political director tweeted a message deriding Baldwin's 'heartland values', accompanied by a video of Baldwin dancing at an LGBT pride parade.
Thompson later distanced himself from his aide''s tweet.
"Now, I am well aware that I will have the honor to be Wisconsin's first woman US senator. And I am well aware I will be the first openly gay member of the US senate," she said.
"But I didn't run to make history," she continued, adding, "I ran to make a difference -- a difference in the lives of families struggling to find work and pay the bills, a difference in the lives of students worried about debt and seniors worried about their retirement security, a difference in the lives of veterans who fought for us and need someone fighting for them and their families when they return home from war, a difference in the lives of entrepreneurs trying to build a business and working people trying to build some economic security."
Baldwin will be succeeded in her house seat by state Assemblyman Mark Pocan, a Democrat who is also openly gay.
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