I rarely book directly with a hotel. In such last-minute situations I have found it better to book on priceline or hotwire. Granted, it requires an internet connection but these days those are not hard to find at airports.

Rarely do I find a hotel cheaper through sources other than priceline or hotwire. And hotwire reveals whether or not a hotel has an airport shuttle, an important consideration in a case such as yours.

Recently when returning from PHX to central MN, I needed a hotel in MSP after a rerouting via DTW. While en route (not sure if it was in PHX or DTW) I secured a hotel through hotwire for my night's stay in MSP. I don't recall the price but it was much cheaper than anything else I could find.

John