In 1994, Burch, then an Ohio state senator, was the Democratic nominee for Ohio governor and he ran to unseat incumbent Republican Gov. George Voinovich. Burch's campaign was woefully underfunded against Voinovich's $8 million warchest and although he campaigned hard, his name never registered with the public and he was buried in the general election, winning only a quarter of the vote and joining his fellow Ohio Democrats in a series of defeats.