It's not really obvious to me. One thing I don't think it can be is the amount of taxing and spending.
Here is a little thought experiment to illustrate the idea that the “size” of government should not be confused with the amount of money the government takes in through taxes and spends through its various programs. Imagine that you live in a country where the government taxes each citizen at a rate of 100%. Your paycheck withholding is, well, your entire paycheck. However, your government has only two programs. First, it takes 1% of total revenue and spends it on a massive monthly fireworks display. Second, it sends each taxpayer a check worth 98% of the amount withheld in taxes. (The remaining 1% is deadweight loss from transactions costs.) So here we have a government that takes in all of the national income and “spends” it all. Yet the government consists only of the Department of Fireworks and the Department of Revenue and Check Cutting. Is that “big” government?
What do you think it means to have a “big” or “small” government?
[UPDATE: Lots of interesting comments and good suggestions below. In his excellent article in Regulation (PDF), Daniel Shaviro of NYU Law distinguishes between thinking of govt. size in “allocative” terms–how much of the economy is directed by the govt.–and “distributional” terms–the extent to which resources get moved around from one person to another. These can come apart. I think this is a useful distinction. But I think the issue about “size” tends to obscure the primary normative issue. If we had a very cheap and efficient govt. that very cheaply and efficiently interfered with almost everything that everyone did almost all the time, the “size” of the impact of govt. on our lives would be huge, regardless of budget in/outflows.
The question is which forms of interference are morally justifiable, or preferable. For instance, Cato's SS reform plan, although in some sense “expensive,” saves trillions compared to the extrapolated status quo. But that's not the relevant issue. And I'm not primarily interested in the fact that money going into and paying out of personal accounts reduces the “size” of government in terms of budget in/outflows. That's interesting only because it correlates with the real issue. What I'm interested in is the fact that a program of personal accounts more closely approximates justice by strengthening property rights over the fruits of one's labor (and thereby enhancing liberty), by helping people to internalize responsibility for their retirements, and broadening the coalition of people with a real stake in the stability, integrity, and growth of a well-ordered market liberal society. If moving toward the achievement of these ends temporarily increased the “size” of government in some accounting sense, I don't think we should be worried. “Size” only matters in the relevant sense of “size.”]