Well, for a theory to "explain most" of anything, how can it begin from a point without any known physical laws?
A "Grand Unified Theory" is often called the Holy Grail of science, but it is not necessary for current theories to be accurate.
A theory does not have to explain EVERYTHING. For example, germ theory explains how we get sick. It does not explain where germs came from.
Quantam theory is able to predict the action of subatomic particles. That we do not understand what every single particle is made of does not detract from the fact that we can accurately predict the probability function of a particle.
Similarly the Big Bang theory explains how the universe is currently, and has predicted future findings. No, it doesn't accout for EVERTHING, but as with all science, since it's accounts for much more than any other hypothesis (like steady-state models for example) it's considered the leading theory.
No, it doesn't explain where the universe came from, but it doesn't have to in order to explain how the universe progressed from the initial expanding singularity to its current state.
To more directly answer your question about the laws of physics breaking down, you should be aware that the understanding that the laws of physics WOULD break down if the universe were compressed to nearly a singularity are based directly ON our understanding of the laws of physics. It's not just saying, "we don't understand it so the laws of physics probably don't apply." It's saying, "The evidence points toward a singularity at the beginning of the universe. Based on what we know about the physical behavior of the universe, many of the seperate forces (strong/weak nuclear, gravity) would become indistinguishable in such a singularity."
Of course, I just realized that may not be what you meant. Perhaps you meant that the Big Bang theory cannot be accurate if it does not explain WHERE the universe came from? If that were the case, then as I said before, germ theory, quantam theory... heck ANY scientific theory would be worthless. Quite simply, theories always have limited scope that is defined along with the predictions that they make.
It's the same reason evolution would still be a working theory if we could prove that God poofed the first cells into existance. No matter WHERE the first life came from, because living organisms reproduce, and copy themselves imperfectly, there IS the potential for speciation and large divergence over long periods of time.
Heck, even if common ancestry were disproved (though it hasn't been) evolution would still be the leading theory accounting for accumulated diversity within "kinds" (which would then have to be defined of course). Over long enough periods of time, you'd see populations diverge enough that they COULD no longer interbreed. But the point is that evolutionary theory (like the Big Bang theory) is not dependent on the origin of life (or the universe). It explains how we got from one point to another, not where the first point came from.