That is exactly what you are going for. They keep a tally on a lot of issues. Unless you are a big employer or influential player in your district, you are not going to get to speak to the Rep or even his/her senior staff.
Unions and some Orgs know that you have thousands of people call your Rep and voice an opinion. Call, fax, or send a letter. Show up to the district office and be nice, deliver your opinion, and hand them a letter.
The last 8 years were driven by the Tea Party doing exactly this. They show up to vote more and practice local politics like everyone should be doing.
So yes, if you are a Republican with a Republican representative then calling them to voice your displeasure about Donald Trump's behavior may be beneficial. Otherwise it probably won't do much unless there really is massive numbers.
I'm in Texas though. A very red state. I've been calling my representative and senators to voice my opinion on all this stuff, but it's hard to tell how effective it is. I either get someone on the phone who sounds like, "oh geez, another angry liberal" or I have someone who just sounds like they'll add my name to a tally or something and says "I'll pass it along" and it's hard to know if they will or if that will help. And then I call my state senator to oppose the bathroom bill going through the Texas senate and the person who I'm talking to on the phone gets borderline combative with me.
I found a group of local people who are trying to do this in a more organized way. I found this[1] the other day and it makes me feel hopeful that our efforts are helping somewhat. We just need to not lose steam. It's easy to get fatigued by this kind of stuff, and we're only a week in.
[1] http://www.sacurrent.com/the-daily/archives/2017/01/26/cruz-...