Going into orbit will be much more challenging than today's flight
To fly a successful orbital mission, they'll need to go about 8 times faster and at least twice as high as they flew today. They'll need more capable life support, attitude control, and especially reentry systems to withstand the heat loads.
That said, if Burt says he can do it and if he has the funding (paging Mr. Allen!), I wouldn't bet against him. I've followed his career in awe for the past 30 years dating back to the VariViggen days. His thought processes aren't even in the same county as a box.