A letter or phone call probably wont have much effect, but actually engaging with them over the course of their term might. The more people who do it the more they’ll respond. Sure politicians will follow the money, but they also know they need to get re-elected if they want to stay on that particular gravy train. If they’re getting the message, loud and clear, that one course of action will lose them votes, they’re more likely to steer a different course, especially if their margin is small. You’re unlikely to see a politician completely flip on a significant philosophy, so I wouldn’t expect miracles, but enough small changes make a big difference.

From their point of view all protests tell them is that a particular course of action is unpopular and will lose them votes, but its a fairly extreme way of sending that message. A concerted effort by even a fairly small group over a longer period has a similar effect. Throwing money at them certainly helps, but isn’t necessary.

To be clear, I’m not American, but, at least currently, the same basics apply, its probably just harder to cut through the clamour to be heard.