I have just redeemed a flight from ORD to DEN on 2 days notice, and reserved to 1st class tickets from DEN to LHR. While there may be a bit less availability of award seats of late, it stills seems very realistic if you have a bit of flexibility.

I also check on another airline for the aforementioned ORD-DEN trip. They had availability in first, but not coach. Still, not bad.