It's too late for a conventional loan now. If you have cash (could be gifted from a friend or relative), or existing "fast credit" (i.e., a family member with a line of credit on a different property), it could still work.
Cash deals can close fast; I've seen two weeks. However, it depends on whether you're in the city or a strict municipality that requires dye tests, occupancy permit inspections, etc. That doesn't go any faster in a cash closing. And, as the other respondents have pointed out, title companies are going to be pressed to the wall next month. If you're in the city, lien letters and final water bills will surely be delayed as well.
I have an FHA that started in late September, scheduled for 11/20 -- and I'm holding my breath :-) I have another cash deal in the works, which would also make the deadline -- but that client isn't a first-time buyer so it doesn't matter. Bear in mind that lots of non-tax-credit-qualifying people also happen to be buying now, and are competing with "credit buyers" for the same loan and title services!
I wouldn't let the tax credit expiration disrupt your home buying plans in any case. If you're qualified to buy and can't get cash together, just buy anyway, expecting not to make the deadline. You might get lucky -- and they might well extend the credit. If they do extend it, it will probably be done in the last few days. They want to avoid having everyone hold off buying, hoping for a higher credit!
Lots of things might happen. It could just expire, of course. Other proposals include raising it to $15,000 and/or expanding it to all buyers (probably still with income limits, I'm sure). You might actually get a higher credit by "missing" the deadline.
Also, the credit depends on your individual tax situation, which can be complex. I think it's best to make your buy/no-buy decision based entirely on other factors, as if there were no credit, then be happy if you happen to get it. Good luck!