The idea of unifying physics isn't new; from what I understand (I'm not experct) we already have unified classical (Newtonian) physics with macro-scale relativistif (Einsteinian) physics, basically by finding classical physics to be medium-scale approximations of relativistic physics.
Now there's quantum theory, with various hangers-on like the string theories, and the problem is unifying the micro (quantum) with the rest (classical and macro) physics.
If you accept the proposition that micro-scale, medium-scale, and macro-scale physics all describe the same continuous universe... in other words, that the universe is continuous as you "zoom in" from the macro scale of galaxies down to the micro scale of the smallest subatomic structures... then there MUST be some form of unifying theory or set of theories. I believe that there is such a mathematical description. I do not quite buy the idea that it's going to turn out to be some sort of concise, telegenic equation that fits on a business card. But any set of mathematical functions which accurately describe the universe at an arbitrary scale would be incredibly useful.
I think that it's likely, provided we can keep our society up and going, that we'll come across some mathematical description. Recall that we have a long history of coming up with one system that kinda works, (retrograde orbits, astronomically speaking) and then only later finding a better model (circular orbit heliocentric solar system model), and later on finding the exceptions and details that point out where reality deviates from our idea model (elliptical orbits, etc) or where there's more going on than we thought. I mean, now we have a pretty good idea how to model a solar system like ours with fair accuracy. It only took us... what? 500-600 years to figure it out? And we're still finding details.
But arguably the hard work was done with the move to the right model -- heliocentric solar system. I figure we'll come up with something similar in fundamental physics -- a besically accurate model which will be expanded upon and refined over a long period.
But the utility and opportunity a Theory of Eveerything would offer is just too tempting. Not that it's omniscience or anything, just near-obscenely useful.