In 2006, even though President George W. Bush supported a hike in the minimum wage (wrongly in my view), the House refused to take it up for a vote. It could have passed with a minority of Republicans joining the Democrats. Those Republicans mostly came from states where there were minimum wage hikes on the ballot. If they'd been allowed to vote in favor of a "clean" raising of the wage, some of them might well have kept their seats, and the GOP might have kept its majority. Instead, the Democrats were swept in that year, and they got the minimum wage hike anyway.