You’ve clearly never called your representative, for any reason. So please stop talking as if you know what you’re taking about.

Representatives have staff. Those people take calls - any call, from anyone. They’re taught and instructed to record constituents opinions on issues like this. You can call, and rant at them for a half hour, and what they’re going to record is incrementing a “no on cloture” tick. When you call about these things, the easiest thing for everyone is to clearly state which issue you’re calling about, and how you want them to vote, because that’s all the staffer is going to record anyway. The representative gets a summary of how many people voiced opinions about which items of legislature.

There’s even a formula: each phone call represents X thousand people who didn’t bother to call but probably agree with the caller. Each email represents Y tens of people. It’s based on how probable or hard it is to contact them.

Now, if you call your rep and want them to, say, work to get Iran to release your kid who went there on holiday and got themselves arrested, then things work a bit differently, and slowly. But the rep will still get the message.

These sorts of calls are statistics and absolutely influence your representatives. They’re what balances the scales, on the other side is usually special interests and quid-pro-quo money that is illegal but it’s never prosecuted because it’s almost impossible to prove.

Voting, and this, is your civic duty. Even if your rep is of the other party - especially in these cases - it’s important to call: you are a voice representing many voters who are too fucking lazy to dial their fucking cell phones, and representatives know this.

What you say is true for online petitions. There’s no evidence these are anything more than email-gathering mechanisms for spam generators, our that they have any effect - but “calling your representative” is “calling your representative’s staffers” and it makes a difference.