First, quantum mechanically a “superposition of states” is just a state, mathematically as valid as any other. It’s like choosing a different “basis vector” — that is, choosing to tilt your coordinate axes when taking measurements.
Second, a cat is of course in a superposition of states, as are we all — because we are made of quantum particles — but these states are very “nearby” in a sense.
Third, only something that is isolated from its environment is really in a “pure” state. In reality we all, including the cat, interact with our environments, and therefore a “true” quantum mechanical wavefunction must encompass both the cat and the environment. If we choose to focus only on the cat, it is in a “mixed state”.
It is because of this interaction that I asserted strongly that a cat will not be in a superposition of widely-separated (dead and alive) states. And if you did isolate the cat from the environment, by putting it in a vacuum, you’d anyway have a dead cat. But this is not a problem only with cats. The main problem with quantum computing is how to maintain the “coherence” of individual quantum bits, or “qubits”, which — in contrast to a cat — are quantum objects with just two states. If it is difficult to maintain coherence for qubits, it is impossible (in this sense of “impossible”) to do so for a cat.
It seems to me that the cat motif serves only to distract from the real question, of whether it is feasible to put a large macroscopic object in a superposition of states — and show experimentally that it is in fact in a superposition of states. With that in mind, here’s a thought experiment.
As in the Schroedinger cat experiment, you have a radioactive atom inside a closed box. If it decays, a detector swings into action — but instead of killing a cat, it moves a screen with a slit in it. On one side of the slit is a point light source. On the other side is a projection surface which is externally visible. So all that we can see is, initially, a patch of light on one side of the projection surface.
So we set up the experiment. Initially, the atom is supposed to be undecayed. But immediately it gains a finite probability of having decayed. So if the screen is truly isolated from the world, it ought to be in a superposition of states — so the slit in the screen, too, is in a superposition of two possible positions. This is a twist on the double-slit experiment but, if the screen is really in a superposition of states, should yield the same result: we should see an interference pattern on the projection surface. Since, as time goes by, the probability of the atom having decayed goes to 1, we should start with a patch of light on one side of the projection surface, progress through an interference pattern in the middle of the surface, and end with a patch of light on the other side of the surface.
We need to do this in as isolated a manner as possible — in a vacuum, near absolute zero — and even then I doubt very much that it is a feasible experiment. To me, it seems the probability of failure is overwhelming, and a failed experiment will tell us nothing. But if it worked and produced an interference pattern, it would be an astonishing result. Anyone care to try?