Can we cut spending in a recession?

One of the reasons I like Ron Paul is because he is practical and compassionate enough to realize that, though he thinks the government is providing services it shouldn't, he realizes that people are dependent on those programs. If given the opportunity Paul would cut the programs, but he would do it gradually.
I bring this up in the context of the tea party fueled Republicans demanding $100 Billion in cuts. I bring it up in the context of 20% increase in CEO salary and an unemployment rate of nearly 10%.
How do you cut spending when the government is the only one hiring? Do you remember that polar bear study John McCain used to make fun of in his campaign? That spending is jobs.
In fact the entire economic strategy for our economy is subsidized by tax money. Both Republicans and Democrats are banking our future on American Innovation. But American Innovation is heavily bankrolled by Congress.
It's because we fund things like studies of polar bears that we figure out new medicines and technology. Medicines and technologies that lead to more jobs down the line. We can not both cut spending and count on the dividends of that spending.
If Republicans have a different route to ensuring America stays ahead in innovation, they have failed to share a convincing argument. De-regulation isn't an area we can compete in. There will always be another country with even lower regulations and standard of living.