This would upend many years of tradition in terms of advise, but I don't see any violation in the Constitution. I'm not sure if that would be sufficient in terms of consent. I suppose it's possible in theory.
It is likely unconstitutional; the President has the power to "nominate" under the Appointments Clause. Requiring the President to pick from a short list of candidates encroaches on that power by transferring part of it to Congress. There are some existing statutes that limit the President's power in this manner, but they're limited to fairly unique positions (the Comptroller-General, which is housed within the legislative branch, and certain local D.C. judges). This Court has generally taken a broad view of the President's power in this area, so I'd expect it to be invalidated.
This suggestion made me think of the question of whether or not the Supreme Court could give the President advisory opinions. This, I believe, was rejected by (I think) John Jay when Washington requested one, but I'm not sure that this would be expressly forbidden (although it does go against the idea of separation of powers).
The Constitutional bar on advisory opinions is traditionally found in the Article III "case or controversy" requirement — the courts are limited to deciding active cases.
