I had the unfortunate circumstance to miss a 1AM connection from UA to US last summer in LAS. As hotels were going to over $200 on a Friday night for a 6 hour stay, the US folks told me about the children's play area in Terminal D which worked out well. It had a nice carpeted floor and benches on the sides that you could set your stuff on or under beside you. A bonus was that there was no speakers for the PA in there, so you didn't get the musack that was playing piped in.
They also brought me down some pillows and blankies from the last flight in and it all worked out until I could get up and b!tch at the UA folks for not doing their jobs.