Obama clearly never said "I promise to keep this plant open"—that much is clear from the Romney-Ryan campaign's own video, no matter how many times the video uses the word "promise" to describe his words. But that's not even the most brazen, cynical aspect of the video. Because here's the thing: Obama may not have been able, to this point, to get that GM plant reopened. But at least he wanted to, which is more than you can say about Mitt "let Detroit go bankrupt" Romney.
Because of Obama's actions to rescue the auto industry (and those of George W. Bush before him), more than a million auto industry jobs were saved in 2009 and more than 300,000 in 2010. Since then, the auto industry has added 200,000 jobs, and GM reported record profits in 2011, standing as the world's largest automaker. None of that would have happened if Mitt Romney had his way. All those jobs would have been gone. GM's Janesville plant would still have been gone, but so would all the other auto plants that are still operating, even adding workers. Janesville would also have lost its GM dealership, what with there being no cars to sell. Toledo, Ohio, would not have gained 1,100 jobs at a Chrysler plant. Workers across the Midwest would not have gotten bonus checks.
So even if Barack Obama had promised to keep the Janesville GM plant open—which he did not—it would be breathtakingly dishonest of Mitt Romney's campaign to take him to task for it. But that's how Mitt rolls.