In the past one hundred years, only 2 cabinet position nominations have been rejected by a vote in the Senate, and neither occurrence was when the President's party held the Senate.
If you look at nominations that were withdrawn rather than going to a vote and being rejected, President Trump has had 5 withdrawn so far which is the most of any President in US history.
I see no evidence that the process is becoming more of a rubber-stamp than it was previously. If you've got some, I'd like to see it.
