There is one massive problem with that idea and that is that this planet has all of the habitable land in the solar system and we don't have a clue how to create habitable land elsewhere.
The US government could easily fund outposts all over the solar system, but separated from habitable land and the natural services that such land provides, like air, potable water, topsoil, nutrients, etc, none of the outposts would survive without continuous supplies from Earth.
Even if we could come up with a magical technology that instantly terraformed all of Mars, that would only give us a few decades of breathing room, assuming exponential population growth. Mars is really small compared to Earth and exponential growth is really fast. If we could somehow magically terraform all asteroids in the solar system then that maybe would buy us another decade or two. In the longer run, barring faster than light travel, the best we could ever hope for is V^3 rate of expansion, since we would be colonizing 3-dimensional space at some constant speed V.