We'll last as long as it takes for the supervolcanoes to go off and the methane deposits in the seabed to get released. That'll raise global temps by 10 degrees. Add that to the potential 6 degrees from global warming and you'll turn Britain into the Sahara.
And the scary thing? The volcanoes are overdue....
Thats how I think we'll die. Either that or a meteor. If neither of that manages to kill us off the Sun will take care of that when it explodes, and if we somehow manage to establish a space empire we'll definitely go down during the "degenerative era" of the universes history, where all the stars will have been reduced to ashen white dwarfs. Should we somehow survive around them, don't worry, they will go out eventually... at which point the black holes will be all that live, and you can't live around them.
There you go, the options for humanity. Die soon, die in the distant future, die in the very distant future or peter on for nigh eternity only to be cruelly snuffed out as the universe falls to pieces steadily under the second law of physics, namely the law of entropy, which states that energy will always go from a state of low entropy, or high organisation (complex molecular structures, particularly solids) to a state of high entropy, or low organisation (at its lowest level, the very particles that make up the atoms.)
So basically we're all going to be protons in the far distant future. Did I depress anyone?
EDIT: If you really want me to put a wager on it, I reckon the volcanoes will kill us. You try surviving when the earth is a blackened, sun-roasted ball of dust.