I would be interested to see the flip side. For weakly affiliated Republicans, what is the effect, if any? Obviously, 136 is a very small sample size, so I won't be updating one way or another based on this.
The sample size here, 136, is not bad at first glance, many studies get published with smaller ones. It's large enough for the purposes here, but you'd definitely want to replicate the experiment a few more times.
Another rule that I use myself is, "multiply p by 10." In other words, a p-value of 0.05 is as good as a coin toss. This sounds outrageous, but seems consistent with reality.