I say no. Here is why.
Criminals are criminals. Most are not smart but do have enough brains to know that if this is how you get caught, try a way to not get caught. Find a hole in the system.
Some argue that we know who our enemy is and there is some truth in that. Most of the 9/11 hijackers were from Saudi Arabia (the Iraq of the 1970's-80's and I am willing to bet by 2020 we will be there even though we support the current régime like in Iraq because the radical elements take over) and the terrorists of the day are Muslim.
So why don't we just stop those who look like Muslims?
Well, for one, then your going to focus only on those who LOOK like Muslims. Guess what the terrorists are going to do? Either get a sympathizer or a Muslim who does not look the part and let him do it. So you end up with another 9/11 and blame the very same people you said should only check Muslims.
Two is that there are other wackos out there and due to the success of the terrorist; do not be surprised that there isn't a homegrown whack job just waiting for people to ONLY focus on terrorists AKA Muslims.
Three, and this is important, is that after all the US is about and what we fight for, are we REALLY going to treat one race/creed/religion differently than another? Granted, I am sure many Mosks in NY were checked out as well as across the country, but to purposely keep someone under surveillance would not only go against our ways, but the very people who we need information from we are alienating.
You would literally alienate the very group you need help from to get these fringe groups under control. The more liberties taken away, the more likely they will align themselves or be benign to the actions of other within their community.
Slowly and surely, liberty becomes less and less, while terrorism somehow continues.