Already exists. It's called "having to get elected next time". The trick is to make sure you find out what their real agenda is so that they have to campaign on that, instead of letting them carpet-bomb your district with litmus-test issues and fear-mongering.
Here's the problem with that statement. Two four-year terms. That's the most you can get. Even if you fuck up the first term, you still have those four years in office. And if you do an amazing job as president? Then you only get four more years. There's no real incentive there to actually DO WHAT YOU SAY. The impeachment laws are total bullshit. That's basically the ONLY thing we have to keep those in power in check, and when was the last time they were actually used effectively? Never. Not once, as I recall, has a president ACTUALLY been impeached. Tried, yes, several have, but none hit that mark. Everyone in the political ring knows it. Once you're in office, you're set. Do whatever the hell you want, because it doesn't matter, and either way, it's over in just a few short years. And even after that? If you were a terrible president, you're STILL a freakin' social figure. I hate this country. I'm getting close to giving up, if I ever get enough damn money to change anything... or move far away... Japan's really freakin' crazy, but it's looking nice right now.
"The eleventh commandment was `Thou Shalt Compute' or `Thou Shalt Not Compute' -- I forget which." -- Epigrams in Programming, ACM SIGPLAN Sept. 1982