This is a big question these days, and many observers say "no". According to Rasmussen, most Americans don't expect GM to be able to pay back the loans. I think the taxpayer is basically screwed here. Even if there is a successful IPO, there is no way that the new GM will be worth as much in stock as the Old GM at its peak.
What could a valuation of the New GM be? According to Dartmouth's Anant Sundaram, the government share could about $26 billion. You can see his analysis here.
So if there is an IPO, and the government gets $26 billion for GM, the U.S. Government will get a return of about 0.60 on the dollar ($50.7B loaned, $8.8B remains as debt, so $42.7B put in as equity)
