Well, less if the power is less, but to qualify as super the character's at least got to be a free-willed tank equivalent. (Unless, of course, the powers aren't useful in a fight. That might raise another slew of questions.)
But unless the government is manned by paragons of rectitude, AND all the superpowered are paragons of rectitude, AND the government officials can KNOW the second -- they aren't going to like it.
Though there is a question of what they could do against it. The people who would stop getting powers because the government doesn't like it are probably the ones they would like to get it, and there would be the question of how easy it is to get powers and how easy it is to lie about it.
If the powers resulted in deformities, death from lack of required secondary powers, or uncontrollable bursts of power -- or whatever produced them generally produced only a few, and harmed or killed anyone else -- they have a moderately difficult jobs, since there will always be idiots. But if the powers are better controlled than that, lies would be their best bet -- if feasible. Unless there was a high chance of dorky powers. . . .