Well, if the policies in question are bad ones (Or if you just think they are), then losing one job in attempting to stop them might well be the responsible thing to do. I'd say the responsibility to support good policies outweighs the responsibility to get re-elected.
If it's a policy that would be obviously bad to anybody, then you shouldn't have to lose your job, because you can explain to your constituents how it is so obviously bad. If you even have to -- they might just recognize it themselves.
The situation you're describing where you would lose your job only makes sense if the law is one that YOU think is bad, but most of your constituents think is good. And in that situation, where do you get off thinking your opinion matters more than tens of thousands of constituents' opinions who you are supposed to be representing?
You are one person. They are a whole district. You don't matter / you're a public
servant.
Oh, I'm sure people would learn to deal with compromises. For that matter, they'd probably lose interest relatively quickly. I give it a couple months before people go back to mostly not caring.
On an ongoing basis? Of course they won't care.
During election time? BAM! hundreds of ads full of painfully misleading bullshit where people now all go run to dredge up anything from committee negotiations that sounds like a politician "flip flopping" and we obscure the things that actually matter even more.
^
That's the best case scenario, which assumes the politicians will give up and negotiate as normal in the first place. Which they might do, as you suggest. I agree. But then again, maybe they won't (or some won't) Maybe they will just stonewall, knowing full well that if they do negotiate normally, they WILL get mud flung at them in the next election.