How long would it take for an illegal alien to get a work permit after getting married to a greencard holder?

If the alien entered US with inspection and became illegal later, then 3 months. If you don't get it in 3 months, set up an appointment to go to the local CIS office and show them the receipt, they will give it to you that day.

If the alien entered illegally whtouth inspection, no right to get a work authorization, and will not get a green card even if married to a US citizen.

If the alien entered illegally, the alien must wait until 245(i) provision gets revived. Current political climate is very conservative. And so, 245(i) is unpopular now. President Bush said "Those who broke our law should not be awarded with green card." He said that even if that law is revived by Congress, he will veto it. So no 245(i) for now. Wait until the President leaves office, and wait more until Congress passes the 245(i) and hope that the next president does not veto 245(i).