That is what the administration has done. Every time the media asks the WH about the things that are going on in the Senate & they are regularly asked, the answer has consistently been "the President asks that his nominees be given an up or down vote." The President's answers have always been along the same lines. They haven't stopped saying it, but the MSM doesn't see the answers as news, so it's not getting reported. Read through the transcript's of a few daily WH briefings.
Blocking Bolton is pure politics, though the left would like to see someone quiet & unassuming in the position.
Perhaps you're right about the media not giving the President's statements much credence if they don't want to hear it. On the other hand, he hasn't been aggressive about bringing it up in public (press conferences, radio addresses, town halls, etc), either.
I have no doubt that there's plenty of behind-the-scenes wrangling. I'm sure the administration has its reasons, I just don't understand the seeming reluctance to use the bully pulpit on this matter. I wonder if the Terry Schiavo matter has made them slightly gunshy. I think that is a possible explanation, or partial one.
If Bolton is pure politics, that seems to me to be a bad move on the part of the Dems, because they will get very little long-term benefit for the disruption they've created. Seems to me they're shooting an awful lot of their ammunition at the Bolton nomination, and will likely be punished for it at the ballot box, at least some ballot boxes.