Actually the question would likely be asked, just as it was with Bush, but it would be different people asking it.
I've heard the martial law theory, and tend to discount it. Here's why.
One of the fundamental truths about Americans is that we are very independently minded, and tend not to follow orders, even from presidents. Since the imposition of martial law would, essentially, be antithetical to the entire concept of America, it is questionable whether our military would, en masse, even follow that order. It would likely result in a split, with a decent percentage of the military actually siding against their leaders, or if you prefer, refusing an order they view as illegal.
Further, one of the arguments that is often used to explain the difficulty of imposing martial law in the USA, even with the military's support, is the high percentage of private gun ownership...if the people do not agree that martial law is in their best interest, then many would resist...forcefully. There's that split, again. So, obviously, gun ownership would be a point of contention if such a plan were in place.
Obama's actions while in office have not curtailed gun ownership, though a few shenanigans were played with ammo availability during the first 2 years. In fact, one of the few pieces of legislation that involved guns, actually expanded carry rights to include concealed carry in national parks.
Admittedly there were "conspiracy theories" about Fast and Furious, and the Aurora, CO shooting that lead the discussion towards manipulating public opinion, the apparent goal being a general disarming of the population, so that martial law could be more easily imposed. But, there seems to be little evidence to back up that belief.
Overall, there is insufficient evidence to believe that Obama will attempt to declare martial law...and assuming the goal would be for him to maintain power, the time to do so would be either right before the elections, or if he loses the election, right before Romney's inauguration.
*If* such stories are true then we will either see it happen, or not, very soon.
The peaceful and amicable transfer of power to an elected successor is one of the foundations of the American system...and we value it very highly. Martial law would be the antithesis of that system. It's *worth* fighting for.