We don't need to invent new physics to do this. The challenges are very real; by various definitions the Saturn V was the most powerful machine ever constructed, and Musk proposes a rocket with several times the thrust. Mankind has not stopped developing spacecraft and rockets since the Apollo era. Whether or not we colonize Mars, we have to start by getting there. I'm sure waiting for a space elevator would be ideal, but if we can do this economically with rockets there's no particular reason not to. We've done this "build a big rocket" thing before. The only thing really standing in the way of it happening again is sufficient motivation. It's not yet extremely politically useful for US politicians to do more than talk about going to Mars, but so far aerospace has proven to be a pretty good source of pork and high-paying tech jobs, and NASA still has a pretty good public image. The only thing we've really been missing is a popular, charismatic leader who can get common people excited about space again. A national threat wouldn't be bad either, but those are pretty easy to gin up.
