Well, since "voting for President" is not provided for under the Constitution, there is no Federal entity with the authority to oversee any processes which would be necessary.
You bring up a good point. Who will count the votes? Rachel Maddow? Wolf Blitzer?
Even more important: Who will certify the result? In the event of a dispute, who will investigate, and audit, the supposed "national popular vote"?
Our current system has each state’s Secretary of State heavily involved in the election process, and I believe, certifying the result. However, it is well known that these results can be challenged in court, and often for a long time.
So, on Election Day, even if the various unofficial tallies show a winner, state irregularities could yield uncertified vote totals in a significant number of states... a half dozen to a dozen, I’d say.
So, what happens... the electors cast their votes for the candidate who is probably president, but while the vote total is still unofficial?
The opportunities for third-world shenanigans boggle the mind.
Fortunately, I too believe that the ban on interstate compacts should hold and make this proposal unconstitutional. But, the legal system has degenerated in the sense of becoming politicized that you can never be certain of any outcome.