NASA is still testing various private replacements for the shuttle and wont have anything working until after Obama is gone.
I suspect that the first president to go into space will be a future POTUS on some form of sub-orbital spaceplane. In fact Ronald Reagan talked about such a plane in one of his SOTU speeches. NASA and DoD spent 10 years looking into the the
National Aero-Space Plane (aka NASP) but ended the program in the mid 90s.
But there are some private companies (like Virgin Galactic) that are now looking at point to point sub-orbital transport. Eventually there will be an Air Force One that can fly from Washington to Beijing in a couple of hours. Maybe in the 2050s or so.