Yes, the media should be scrutinizing those claims, and yes Romney will probably be shown to at least be making dishonest claims if anyone with resources ever cares to look it up. No, the first probably won’t happen, and if it does it’ll be in a couple page A-17 articles that no one will talk about.
But it’d be harder for him to make that sort of stuff up if Obama had been pushing on jobs for the last couple of years instead of pivoting to debt. It’s not like Obama tried his hardest and got some results. Instead he passed one bill, said it’d be big enough, declared victory, and is now being accused of doing nothing. “But he did some stuff for a few months” isn’t good enough of a response.