The Republican party has been advocating a cut in spending which would only result in further slowing of our economy that is still showing signs of damage from the financial crisis of 2008. If the Republicans had their way we would be addressing the deficit issues at exactly the wrong time because economics has shown that deficit spending in a recession helps stabilize economic growth.
He would deregulate and run the United States like he did a lot of his businesses. The problem is that he was professional company flipper that left a wide trail of ruin in his wake for most people, and that's not really the kind of thing that makes me confident in his abilities to run the nation.
Trickle down economics and deregulating don't work. They're what got us into this mess to begin with. Even if there was some kind of better recovery due to him, it would only be another gigantic bubble.
Our economic recovery would not be better under Mitt Romney. We would actually be further along if the Republicans would stop stalling everything in Congress and to quit filibustering every bill brought up by the Democrats. The stimulus package would have worked had it been larger and used for what it should have been. If the Republicans would had signed on a couple years ago to rebuild roads and bridges sooner we would be out of this mess.
I do think in the most technical sense Romney could have done a lot to fix the economy as a whole, but it would have involved picking a group of people to completely screw over and doing so. The numbers overall for the country would look a lot better on paper, but he'd bury some people to get them without a second thought.