Bold strategy. Let's see if it works out. I rather think that if you don't participate, then you're effectively not included in the set of people whose interests are considered by politicians when they form their campaign promises. When you do this, the median is likely to shift right, not left as you think, if you take a moment to recall the definition of median. Sometimes we are placed in tough positions with few good options but still having to select one.
I would propose that a lot of the cases of Dems appearing to renege on campaign promises are the result of closed door deals with the other factions where they're forced to make compromises in order to get some of the things they (and you) desire. We're not privy to those deals because it would reveal to the voters that the politicians abandoned one wish for another and a competitor would use it against them in a primary, and then there would be no deals and Congress would grind to a halting stalemate.