Spending has gone up with both parties in control of the presidency or the congress. The main difference between the Democrats and the Republicans is that the Democrats raise taxes when they spend more, but the Republicans don't. Here's a nice write-up on the national debt over the years:

http://www.cedarcomm.com/~stevelm1/usdebt.htm

Unfortunately, he doesn't provide inflation-adjusted graphs, which would be interesting.

This is one thing I find funny about "political sloganism" - the Republicans always talk about "tax and spend Democrats", but never talk about the fact that the republicans are the "don't tax but spend anyway" party. As an individual you can't spend money if you don't make money, and there's no reason for the government to be any different. (and many reasons for the government to be the same - read "The Creature From Jekyll Island" by G. Edward Griffin for a lot of interesting information about how the financial system works)