You are absolutely right. I am Jewish and, if I were there, I would probably overlook the differences.
At the same time, I could also pose that question to the Christian friends: is this the time to emphasize differences? What would be wrong to pray in the name of G-d in a mixed company?
I've been at inter-religious services, and the Christian ministers alway found the unifying prayers.
You too would feel funny if a rabbi asked you to join him in a prayer for release from the Babylonian exile or some other particularity of Jewish faith. I would call such a rabbi stupid and definitely divisive.
So, you may lament that the senators did not overlook the remark, but you should also question the insistence of the minister. He says that the New Testemant compels to pray in the name of Jesus. Firstly, I doubt that he compels to pray in the name of Jesus only. Secondly, since thousands of ministers in similar circumstances found other prayers, does that mean that they are all wrong and he is the only pure one? YOu may question his wisdom in driving the wedge where there is none.
For example, there's the issue of headgear in church, or during prayers. Most Christian groups don't come down on it one way or the other. Some believe that headgear is idolotrous.
The deal is that if Mr. Miller and other bigots want to keep hard-core fundamentalist Christian ministers out of the Maryland State legislature, all they have to do is make the "In Jesus Name" business a big issue. Notice that Miller blames it on the Jews - we fully expect him to acquire a monopoly on the sale of armbands in the near future.