This has happened to me a few times, generally when it has gotten colder than I had planned to sleep in my hammock. The suggestions given are really good, and as Shug says, one night won't kill you. I did, however, decide to just get up and start hiking at 4am on one solo trip I was so uncomfortable. The other time I was using a PeaPod and I wound up wrapping myself in my tarp as a vapor barrier then wrapped up in the PeadPod and was ok.
I can also say that if you have whoopies and straps you can manage some creative hangs on the AT in shelters. This was from a AT Shelter in VA in 2011.
I hung inside that night due to heavy rain and the ground around the hanging sites all being underwater - I wasn't worried about my hang, I was worried about my shoes!