I should have noted in my post below that the 5-to-7-million American Muslims estimate was one of the higher-end estimates. Estimating the Muslim Population in the United States by Tom W. Smith of the National Opinion Research Center (2001) reports that
The best, adjusted, survey-based estimates put the adult Muslim population in 2000 at 0.67 percent or 1,401,000, and the total Muslim population at 1,886,000. Even if high-side estimates based on local surveys, figures from mosques, and ancestry and immigration statistics are given more weight than the survey-based numbers, it is hard to accept estimates that Muslims are greater than 1 percent of the population (2,090,000 adults or 2,814,000 total).
I haven’t examined the matter closely myself, so I don’t have a truly informed opinion. But to my knowledge, Smith is quite well-regarded in the field, and is the director of the very well-regarded General Social Survey. So at the very least the 5 to 7 million American Muslims figure should be viewed with some skepticism, recognizing that the number might be 2 to 3 million instead.
UPDATE: Thanks to commenter wm13, here’s a 2007 Pew Research Report estimating the number at about 2.35 million. Pew, like the GSS, is a well-regarded survey organization, which to my knowledge has no axe to grind on this issue.