I don't think he does - the facts that he hadn't bothered to write it, hadn't bothered to lock on a Democrat Congresscritter to bring it up, and that Harry Reid hasn't scheduled an actual quick vote on it are rather indicative. Obama at this point is out of arrows - the Stimulus failed to do what he thought it would do, the Fed is tapped. He's not going to be able to seriously lower unemployment or increase growth between now and 2012... so what he needs instead, is a counternarrative. He needs a foil so that he can campaign on "If Only They Had Passed My Bill We Would Be In Recovery Right Now"... but (critically), they can't actually pass it, or else the jig is up. So, you pay for the whole thing with tax increases (which you know Republicans will refuse to do), in order to poison-pill it, and viola - you have a campaign stump speech to run against Congress with.
Again, though, they can't pass the bill. If Republicans introduce and pass portions of the Presidents' Proposals (say, the Trade agreements and the Payroll tax extension), then it puts Democrats in a tough bind. Either the Senate sits on it, which severely degrades the ability to run against obstructionist Republicans, or it passes, and it moderately to severely degrades the impact of the "darn them they won't do what I asked" motif.
A Risky Play by the President. We shall see how it turns out.