Rubio wouldn't take the job for King. If he runs and loses the nomination along with his senate seat, he'd probably take the VP spot for a more credible candidate, but more likely take a run at the governorship in 2018.
I think the most likely VP for Peter King would be Bobby Jindal or John McCain. Jindal wants to be president really bad, and a doomed to fail vice presidential run would likely be the only way to keep his name in contention for 2020. He also adds to Kings ticket as much as anyone else.
McCain also really wants to be president, and may actually take the job of VP if offered. Yeah he's 80 so it's not likely, unless you consider that nobody would want to be attached to King unless they literally had nowhere else to go. McCain is Kings ideological twin.
I think you nailed it. Anyone want to make a Hillary/Kaine (or whatever) v. P. King/Jindal map?