NFA type regulation of handguns would present serious, and likely insurmountable, Constitutional challenges. In United States v. Miller, SCOTUS ruled that the NFA was not in violation of the 2A because the weapons it regulated (a short-barrel shotgun in the case of Miller) were not "in common usage nor particularly suitable for usage" by the militia and thus not afforded protection by 2A. In Heller v. District of Columbia, however, SCOTUS specifically ruled that a handgun (a 1911 in the case of Heller) was "in common usage" and "particularly suitable" and thus fell under the protection of 2A.
So, from these two cases we seem to have a precedent that the NFA is only constitutional because it applies only to weapons which are not of a class protected by 2A. This would seem to imply that it would be unconstitutional for NFA regulations to be applied to weapons of a protected class and, per Heller handguns are most certainly of a protected class.
Now, so-called "assault weapons" may or may not be of a protected class as SCOTUS has said nothing about them. Justice Scalia did mention in the Heller decision that "dangerous or unusual" weapons could be heavily regulated or banned, but he left what exactly constitutes a "dangerous or unusual" weapon ambiguous. That being said, even if "assault weapons" are ruled to constitute a "dangerous or unusual" weapon, the only way that I can see handguns being able to qualify as "assault weapons" would be in the cases of very specific types of handguns which have very distinguishing features setting them apart for other handguns. For example, I could see AR and AK pistols specifically being banned or made NFA weapons much easier than I could semi-automatic handguns in general.
Smith, and Wesson, and Me. -H. Callahan
Well waddaya know, one buwwet weft! -E. Fudd
All bad precedents begin as justifiable measures. -J. Caesar