Yes and no. The NSA's activities in foreign signals intelligence is something every modern military does, and is legal under the constitution. However, the NSA's domestic spying (weren't they caught tapping directly into internet backbones in 2007?) is a violation of the 4th amendment and is more like something secret police would do. Ron Paul is one of the few people who holds this position.
"Small government" doesn't just refer to the government's budget, number of employees, percentage of GNP, etc. It also defines a sharp limit to a government's involvement with private aspects of citizen's lives. I have read some compelling arguments for increasing or maintaining the size of gov't social programs (sometimes big gov't can be good), but I've never agreed with people who think domestic spying is good (that kind of big gov't is always bad).