Bacchus, you're right that the NRA postcards are short and recognizable. They're recognizable as a knee-jerk response from a well-mobilized body of people who are committed on this issue -- in other words, an entirely predictable group. Elected officials know even before the postcards arrive that anti-gun bills will produce this kind of canned response.
A rational, well-thought-out letter, however, can't be pigeonholed as easily, and the recipient doesn't know if it comes from a True Believer or from a fencesitter who has been persuaded by logic and reason, and whose opinions on other issues -- and of the elected official's actions -- are less predictable.
Politicians already know the responses that their actions will provoke from extremists on both sides of an issue. What concerns them is the response -- and the size of that response -- from the voters in the middle.