It's a straw-man argument. Big government/little government are not the reasons. Nobody (I haven't heard anybody. They may exist though.) said they do or don't like Mexico because of big/small government. That is not the only reason to go to or like Mexico.
It would be like saying; since the people of Arizona don't like Mexicans why would anybody from Arizona go to Mexico?
And saying that Democrats are the only ones who "like big government" is not accurate either. Government grew under Republican leadership from 2002 - 2007. I would say that I want the government to regulate Wall Street and the oil industry and pick up the trash and make sure food is safe and build good roads and make sure water is clean and make sure that medicine does not hurt me or... that kind of thing. I would like to see the military budget downsized by 50%. I might want to see farm subsidies reduced or eliminated but I would listen to the argument for and against. There are things that people want that I may not want. When somebody talks about "big government" it would be a good idea to give examples.
I wonder what a small government person would want to see cut. In May Eric Cantor
rolled out a campaign called "YouCut" which promises that House Republicans will call for spending cuts chosen by online voters. It turned out to be a little more difficult that they thought.
A 62 year old Tea Party supporter acknowledged to the Times when she was told that if defense, Social Security, Medicare and the required interest on the national debt are untouched, that's over $2.2 trillion. Somehow, Tea Partiers would have to magically cut $1.3 trillion of the remaining $1.6 in FY 2010 spending. She said:
"That's a conundrum, isn't it? I don't know what to say. Maybe I don't want smaller government. I guess I want smaller government and my Social Security." She added, "I didn't look at it from the perspective of losing things I need. I think I've changed my mind."
So the point is that there are a lot of people who say they want "smaller government" (this seems to be buzz words from the right wing talking points) but when asked what they would cut they have a hard time.