I love the space program as much as anyone, but there is not even time left on habitable Earth to think somehow a colonization to Mars would save us.
Terraforming is a VERY difficult, expensive, and risky task, easy to fail at, as writers of hard science fiction like Kim Stanley Robinson have explained in fascinating detail.
If you REALLY want an uninhabitable planet to rehabilitate, take the engines out of existing rockets, put them on cinder blocks, and wait. The wait won't be long. You'll be on one faster, cheaper, and more reliably than if you try to escape the gravity well, and with lots better available resources.
Seems far better to me to just get started now in earnest with the serious task of fixing Earth, in hopes of optimizing out the messy, sad, painful part in the middle where humanity goes extinct due to that messy uninhabitability thing that's rocketing toward us. Fixing things here at home is perhaps not as flashy as planetary colonization, but it's much more relevant and, if we start now, doable. YMMV.