Yes, there are problems
First, getting out of the atmosphere is the comparatively easy part of going into orbit. Getting a rocket to travel a hundred or so km straight up so that it is effectively out of the atmosphere is not that difficult, getting it to travel "sideways" at the 7.8 km/s required to achieve low earth orbit (LEO) requires enormously more delta v. If you look at the old Space Shuttle launch profile, the Shuttle was outside the denser sections of the atmosphere (altitude approximately 50 km) at the point of solid rocket booster (SRB) separation but "only" travelling at 1279 m/s. It needed to accelerate for a further six-and-a-half minutes to (almost) achieve LEO. (A final correction burn was required in order to achieve a stable orbit.)
(Note that while the SRBs made it to an altitude of 50 km under thrust and continued to a peak altitude of 67 km on inertia, they then fell back to Earth and were recovered for recovery. Getting to altitude did not get them into orbit.)
The two SRBs combined massed 1,180,000 kg and were more than half the mass of the shuttle at launch. So can you equate your forcefield generator to the SRBs and say it does the same job? Unfortunately, no - the SRBs also provided structural support to the fully-fueled orbiter + external tank and provided most of the thrust to not only clear the lower atmosphere but to get the shuttle up to almost a sixth of the necessary speed to make orbit. The rocket equation is painful - you need more fuel at the start to accelerate not only the payload but also the fuel you will need later. Unlike the SRBs, the forcefield generator is presumably retained as part of the shuttle, which means that more fuel will be required in order to accelerate the shuttle later in its flight profile, offsetting any savings in the early part of the launch. So unless the forcefield generator has a negligible mass, it probably isn't going to help much.
A second problem is structural. While the lander was designed to glide and land like a conventional aircraft, the combined structure at launch could only withstand very limited lateral forces. You cannot simply weld a big ring onto the top of the shuttle and lift the combined mass from that point, the craft would disintegrate. In order to make the structure "liftable" from some arbitrary point where the forcefield generator is mounted, a huge amount of structural reinforcement will be required, which will increase the total mass of the craft, which will increase the fuel required to accelerate it, which will increase the mass further... This is one of the main reasons why various real-world proposals for piggybacking launch vehicles into the upper atmosphere using balloons or conventional aircraft have been abandoned as infeasible.
Third, in order for any decent size shuttle to become buoyant, it needs to be displacing a truly huge quantity of air. If we continue to use the old space shuttle as an example it had a mass of over 2,000,000 kg at launch. Given that a cubic metre of air at sea level has a mass of 1.29 kg, this means that the force field needs to push the air out of around 1,550,000 cubic metres of space at sea level.
As it ascends and the atmosphere becomes thinner the forcefield needs to keep increasing in size to compensate. At a height of 50 km, the atmosphere is approximately 1/650th as dense as at sea level, so it will need to maintain around 1,000,000,000 cubic metres of vacuum.
Assuming that the forcefield is spherical and centred on the shuttle - what happens when the shuttle is sitting on the ground and the forcefield is turned on, with half the sphere underground? What happens if solid objects impinge on the forcefield? (Maybe the bottom of the sphere should always be just above the shuttle, just an idea.) A significant issue if the shuttle is inside the sphere, as described, is that it is totally at the mercy of the weather during a long ascent. If it fires its engines at all it is effectively just redistributing its mass within the sphere rather than actually changing its vector. Along the same lines - very important to turn the forcefield off before firing the main engines!
In summary - even if this technology did exist, unless it had negligible weight and power requirements it would probably cause more problems than it solved in launching a shuttle. There are plenty of potentially great applications of this technology, but that is outside the scope of the question.