Any president with the balls to stand up to the unions, and the political will to do it, could make severe cuts in the executive branch departments. You're also underestimating how effective veto power can be in the hands of a president willing to use it aggressively. There's also an often overlooked authority that any presidential administration has, the Vice-President is the President of the U.S. Senate, the Constitution says so, and Ron Paul knows the constitution. Every VP has the power to set the legislative schedule in the Senate, but I can't remember the last time it was used in this way, the VP is much more than a tie breaking vote.

Here's a good video.