The infant will need a passport, though I think just the birth certificate is okay if traveling overland.
Not sure how long it takes to get a birth certificate...presumably that depends on the jurisdiction.
It takes about 4-6 weeks to get a US passport, but you can get it expedited, about 2 weeks.
http://travel.state.gov/passport/processing/processing_1740.html
Traveling within a few months of birth is probably feasible from a timing perspective. But personally, I don't think it's wise to travel with a two month old infant in winter from an exposure to disease perspective...less of a worry if they're driving up in their own car.