As a figurehead yes and they sometimes even get a few things they want in the budget, but 99% of the budget spending process is congress. To place the blame on any president is foolish. Yes I know that places the blame on just as many Republicans as it does Democrats but it is how our system works.
If the President agrees with the spending, then he signs it.
If the President disagrees with the spending, then it his duty to veto it. If Congress wishes to go against the President, it may do so.
So therefore, the President takes part of the blame directly by placing his signature on the spending bill.
A large part of the Reagan cult can't seem to accept that.