In response to the economic crisis, the Republicans would effectively do nothing. You'd have a cutback and spending freeze on everything minus defense spending, which would probably rise, as it has under President Obama. Tax cuts will increase the deficit substantially, but that will be of little care to the Republicans and McCain.
All of this probably won't bode well as unemployment rises steadily. No spending means no priming of the economic pump and a worse over all economic trend. I would probably predict that financial bailouts continue (McCain had every intention of supporting them back in the campaign, after all), while GM and Chrysler go through bankruptcy. The latter will matter little to the Republicans, who have pretty well given up on winning the midwest in the near future anyway.
The McCain administration might try to privatize a few more governmental services under its watch, too. You can forget the sort of cap and trade legislation under construction in the Obama administration--if a system is put in place, it would give a grandfathered amount of pollution credits to already pollutant-wealthy energy corporations. Big oil will have a field day.
With regard to foreign policy, I don't see much of a change from the Bush administration, beside a small polishing of America's image. McCain is much more of an internationalist than was Bush, after all. Guantanamo probably closes on schedule, but the suspected terrorists housed there aren't going to get anything resembling a fair trial. Torture might end up being banned, too, but with Conservative Republicans in control of Congress, I doubt it.
Iraq will probably progress as OTL, but I could see increased violence if the McCain administration doesn't agree to a timetable for withdrawal. Saber-rattling will continue in the region, of course. More verbal assaults on Iran, et al.
In Afghanistan, I'm not sure what happens, to be honest. McCain never really had a well defined policy position on what to do about that war, and with the Bush administration's track record of ignoring it, I'm sure that we might see something similar from a McCain administration.