I doubt it. To make it work, you need leverage. Make citizen's life slightly easier or slightly worse based on his score.
Worse access to credit, withholding from top universities, preventing from starting a business - not easy to do anything like that on a grand scale in market society. So you won't exactly be making a new citizen.
This sounds exactly what Experian does. They are used by most (all?) UK banks to validate your credit score and they also provide an "identity protection" service. If your score is too low with them you don't get any credit anywhere.
1. Require that all banks have insurance for accounts that are unable to be FDIC insured but are under $200,000.
2. Legislate that credit scores take into account a score determined by Homeland Security, under the premise that homeland knows more about a person (e.g. do they gamble in monaco off books a lot? are they involved in a radical movement and likely to lose or give their jobs? are they a likely to be arrested?). If the public needs more sell on this use the canned like "Do you really want your bank to lend money to terrorists?".
3. Drop FDIC insurance for any bank that operates outside of #2. #1 will force these banks to buy insurance, lowering their profitability. At this point, the system self-regulates and is hard to dismantle.
Score is still "go" vs. "no go". You can only shut off so many people because parallel "grey" finance market arises.
More finesse is needed. You can try banks to offer different deals to identical (finance-wise) people based on their HS score, but they're probably sue.
I'd be surprised if the US didn't already have a database somewhere with scores indicating the likelihood of you being a terrorist which probably has a bearing on the likelihood of you getting stopped at an airport or put on a no fly list. Not the same as the Chinese proposal but something along those lines.
US security forces can affect things for the average person, just not the same things that China can. Not credit scores at the moment (well not legally on a mass scale), but they can for example put you on a no fly list; or if you're a non US citizen and they didn't like your "facebook" score, in this hypothetical system - they could deny you entry to the US.
So yeah this is more than just monitoring, I just called it that to distinguish it from the large scale behaviour shaping China seems to be toying with. Even having such a system in place, however, makes people behave differently: google "panopticon".
Worse access to credit, withholding from top universities, preventing from starting a business - not easy to do anything like that on a grand scale in market society. So you won't exactly be making a new citizen.