Eventually, we do need to leave.
But I think that will be sometime before the Sun enters its [link|http://en.wikipedia.org/wiki/Red_giant|red giant] phase. But Mars probably won't be far enough away to make much of a difference, and the Moon certainly won't.
Some of the problems with the psychology of small groups can probably be addressed if necessary (e.g. doping the food), but there are things like loss of bone mass in reduced gravity that may be more difficult to compensate for. Our bodies have had a very long time to adjust to our particular g and we don't really know how we'd do on Mars or the Moon where gravity is much less intense. And that's one simple thing that we do know something about. What about the circulatory system? Are the risks of [link|http://en.wikipedia.org/wiki/Pulmonary_edema|pulmonary edema] higher? Stroke? Infectious disease? Etc.
As Andrew indicates, it costs a lot in terms of infrastructure and energy to get stuff out of our gravity well. Apollo cost an estimated [link|http://www.speculist.com/archives/000662.html|$105B in 2003-dollars], and those were very short duration missions that only moved a few thousand pounds to the Moon. You're talking about a project that is orders of magnitude larger. Even a few women in a colony will need a large support infrastructure there (they won't be able to do much while they're recovering from childbirth).
For the next few thousand years, it's hard for me to imagine it being better to have large-scale settlement on another planet than living here. Even if we have to build something under the ocean because the ozone's gone or because everything's too radioactive, it'll be cheaper here.
My $0.02.
Cheers,
Scott.
(Who thinks that small-scale settlements are a good idea, but not because we need to leave Earth soon.)
