Maybe it helps to look at some figures. Here's the 2009 Heritage Index of Economic Freedom top 10:
Pay special attention to Denmark at 8th, which is closer to the U.S. at 6th than the U.S. is to Ireland at 4th. According to the OECD, Denmark's government spending as a percentage of GDP is 50.8 pecent. In the U.S. it is 36.6 percent. Now, note that size of government is an input to the formula that determines the ranking. Denmark takes a HUGE HIT for that in the index. No country in the top ten has that low a score on any dimension. In fact, they take a big hit twice, because tax rates are in the formula as well. Drop the size of government from the index, but keep the tax rates (i.e. “fiscal freedom”) and Denmark would score higher than the U.S. in economic freedom. Of course, Denmark, like the U.S., gets high marks in other rankings focused on political and civil liberties, like Freedom House's. Denmark may be culturally weird, but I think it counts as a possibility proof of very big but quite limited government. Like the Economic Freeedom rankings, you might think that such high tax rates and big government count heavily against them, but it remains that they do nearly as well or better than every other country in the world in every other aspect of economic freedom. Tax rates and government size are in fact dissociable from regulation, barriers to trade, and so forth.
Now, I'm just trying to reinforce a conceptual distinction. I'm not for one second arguing that the U.S. should have a bigger government. I think we'd be much better off in the extremely lean neighborhood of Singapore (about 15% I think). But I also think that the size of government in the U.S. is less important than some other aspects of economic freedom, and less important than the composition of spending, some of which is both immoral and wealth destroying.
Consider that Denmark's size of government is similar to that of France, which scores 64th in Economic Freedom, between Uganda and Romania. The implication is that France could become immensely more economically free without doing much by way of cutting the size of its government. The way to do this would be to severely limit, as Denmark has done, the ways in which the government may intervene in the economy. Likewise, holding size of government constant, the U.S. could be doing much better, though I'm afraid we're rapidly moving in the other direction.
More fun facts! Hong Kong is part of communist China, and so is lacking much assurance of liberty. Singapore is more or less an authoritarian technocracy. We don't hit a liberal state until number 3. Australia, at 34.9 percent of GDP, has a smaller government that the U.S., as does Ireland, at 34.2 percent, while New Zealand is a bit bigger at 39.9. Switzerland is also smaller (35.4%) but the rest of the list is bigger. Canada is in the neighborhood of New Zealand, Denmark is WILDLY larger than the rest of the list, and the U.K is very big at 44.6 percent. The only countries in the OECD with bigger governments than Denmark is are France (52.4%) Sweden (52.6%), and both do have fairly dismal economic freedom scores. However, Sweden seems to have the right idea, as it has refused to bail out SAAB.