I think Obama benefits relative to the 2012 election since I think he could run against a do-nothing GOP House
No. If anything, winning the House benefits the GOP. Remember, Obama's already unpopular now, in 2010, even though his party already controls everything. If something is still wrong two years from now, that's a bad thing for Obama because the Republicans could portray him as not being able to get anything done no matter who runs Congress.
And if everything
is OK in 2012, then the voters will likely just retain the status quo, so the GOP House isn't a "bad" thing for Republicans no matter what.