I'd say when (if) they start doing things that only NASA does and demonstrates that space exploration can be done better privately. Then the bureaucrats in all space-related agencies will start demanding regulations in order to create some space-related state monopolies so they get to keep their jobs. Companies such as SpaceX might soon start to embarrass governmental space agencies and prove them unnecessary in more and more areas.
Pretty much the same what's happening with the war on drugs. It doesn't matter if there is not any reason to have it, because thousands of police agents and bureaucrats have their livelihood at stake on this, that's why they'll necessarily identify their personal welfare (aka not getting fired) with the common good and make arguments in favor of it.
I think the turning point will be before reaching Mars. I did read somewhere that Musk had planned sending manned trips to Mars and there was some talk on funding some colonies there. They announced it for a date fifteen years before NASA's plans. I think it is delusional to believe that government is going to allow private enterprise to reach Mars before they do.
I really wish they (SpaceX) did it. It would shut millions of statist mouths.