I know my state representative and senator are accessible; I've had email conversations with both in the last couple of months. I've never contributed to either of their campaigns.
However, there's an obvious difference when one sends letters or emails to the federal level. When I've gotten responses, it's always been at least several weeks later, and sometimes several months. The messages I've received have been loosely related to my original message, but they have never addressed any actual point I might have made. I'm not feeling the love.
Politics is also a hierarchy and its worth keeping in mind that local politicians may have much better connections to people in the next tier than you do from outside. Your local state senator may have much better access to your federal senator and that level of access can turn into opportunity for them to influence them. If your state representatives know how important their behaviour with regards to federal issues is to you as a voter, you stand a much better chance of the system working how it's intended.
It's systemic lack of involvement that's causing the most issues in American politics. From the top with "lifetime senators" largely immune from their constituencies, and from the bottom with voter turnouts under twenty percent.
However, there's an obvious difference when one sends letters or emails to the federal level. When I've gotten responses, it's always been at least several weeks later, and sometimes several months. The messages I've received have been loosely related to my original message, but they have never addressed any actual point I might have made. I'm not feeling the love.