The attacks on "big government" have created an atmosphere, a meme, has activated certain frames... It's too widespread with too little effective push-back.
Here are a couple of quotes from Pres. Obama's 2013 State of the Union address:
"It is not a bigger government we need, but a smarter government that sets priorities and invests in broad-based growth."
"The American people don’t expect government to solve every problem."
Obama isn't really pushing "small government" - at least not in the way or to the degree some are. But his wording is still likely to activate brain routines which will make some listener lean more towards small government.
He could have said something more like:
"Our government needs to be smarter, that's the real question - not the size."
"There are problems which can't be solved without government, there are some which can be most effectively handled by government, there are some problems which democratic norms require be run by the bodies elected by the citizens, and there are some which do not need to be in the hands of the government."
The anit-big government / pro-small government message is, in many ways, a ruse. Not that many people want to have a small government when a foreign government invades, or when a natural disaster strikes, or when their home is burglarized, or when an unlicensed driver totals their car. Strong majorities oppose cuts to Social security (they don't want small government when they retire). How many people wanted a small government which provides no unemployment benefits when the economic crisis hit? How many would want to live in a community with no public schools?
It's not about "small government" - it's about low taxes for the more affluent who don't expect to need public services, and fewer services for those who the more affluent don't expect to rub elbows with. Multi-trillion dollar bail-outs of billionaires are OK, a little help for those living in poverty because of stingy wages and benefits given by those same billionaires to their employees are not. This is one of the images we should be projecting of the "small government" advocates.
We need to present a different view in more effective ways.
When you go to buy a car, you don't just pick whichever one has the smallest price tag. You look for which meets your needs and gives you the most bang for the buck. That's the smart way to decide how much taxes you pay in order to get which benefits for yourself directly and for society (which is for you indirectly).
If you were looking to sign up with an organization like the Auto Club (AAA), you probably wouldn't want to sign up with the smallest such organization. You'd want an organization with lots of resources and which was available in lots of places to help you wherever you and your car might be.
At least for some things, you'd rather shop at a store with a bigger selection rather than a small selection. And even if you like the idea of shopping at a small, local store, you might also know you can get some things more cheaply at the big stores - because there are advantages to being big.
According to studies discussed in Scientific American, the health care provided in Canada's single payer system is similar to that in the US, but Canadians pay a far longer cost per person. "Big government" in ways like that can save the people's money, "small government" can cost you more. If the US instituted a single payer health care system, it should be able to do it at a lower per capita rate than Canada, because the US population is something like 10 times that of Canada. A population 10 times as large probably only needs 9 times as much administrative costs. Bigger has advantages.
We need to develop the best of these kinds of analogies, narratives, frames, etc. We need to make it "common sense". We want to make as many people as possible ask themselves what the consequences will be when they hear "small government" talk. When they hear "small government", their gut reaction should be, "Why would I want that?"
So, put on your thinking caps and start working on the best way to message this.