You don't need NNTP, just HTTP. You can get the time from NIST using the code at this node. It should be trivial to integrate the two bits of code together into something acceptable.
What would be even better is to use whatever NTP / NIST time-getting solution to set your computer's clock; that way, not only this, but every other time-referencing program will have the right time.
There's a reason time() is a system call.