Yes, but, as they say "the constitution isn't a suicide pact" and if the only way to stop mass terrorist attacks in the U.S. is by trashing the fourth amendment, the fourth amendment will get trashed.
Unfortunately, if this is the case people will probably only realise it after the first serious mass terrorist attacks.
Yesterday I was using the Global Terrorism Database to check some suprisingly low figures on what percentage of terrorist acts are committed by Muslims. (Short answer: Worldwide since 2000, about 80%, rather than 0.4 - 6% as given in various sources.) But I found some odd patterns in the data for the United States. Look at this chart of terrorist acts in the US which meet GTD criteria I-III and are listed as "unambiguous":