Falcon XX

This may not be the case, because the Wikipedia says that it is unconfirmed. So, take it with a grain of salt. The speculation is that the Falcon XX may use a nuclear thermal upper stage, which is what almost took place in the Apollo program, which put 12 men on the moon.

The NERVA rocket would also be a nuclear-powered upper stage for the Saturn rocket (the Saturn S-N), which would allow the upgraded Saturn to launch much larger payloads of up to 340,000 pounds to Low Earth Orbit.

Also:

The engine was deemed adequate for Mars missions being planned by NASA. The facility was also deemed adequate for flight qualification and acceptance of rocket engines from the two contractors.

So, you see, NASA already had capability to get to Mars in the sixties, but the program was canceled.   If Spacex revives this, they just might make good on their plan to get to Mars in the next decade.  If the government really wants to get to Mars, why not contract with Spacex in order to get the job done?  Most likely, it can be done under budget and on time.