Early in the shuttle program, it was assumed that the space shuttle would be a 2-stage reusable vehicle. The first stage would be a manned flyback booster, and the orbiter would be the second stage with internal propellants.
There were two problems with this.
One was that the orbiter would have to be very large, since it was carrying all its own propellant. The eventual solution was to put all the propellants in an external drop tank, our beloved ET.
The other problem was that the flyback booster would be the largest aircraft ever built, much bigger than a 747, with the ability to reach hypersonic speeds and altitudes near the edge of space, and it had to do this with the orbiter on its back.
The solution to that problem was, again, to reduce the size of the orbiter using an ET, and to ditch the manned liquid booster and substitute a pair a SRBs. The SRBs could always be upgraded to liquid flyback rocket boosters (LRBs) if the money ever became available.
Here's a picture of the early shuttle concept I just described. Note the enormous size of the booster plane:
http://astronautix.com/graphics/s/shutbnar.jpg (The hotlink is blocked by astronautix; paste it into your browser window to see it)
---------- Post added at 12:02 AM ---------- Previous post was at 12:01 AM ----------
BTW, the answer to the above question is "maybe, but it would be a technical challenge".