Maybe sometimes. I think that lots of people on the left feel vulnerable somehow and want the government to be their supporter and protector.
Some of the newer leftists feel this way because for years the government has actively opposed them - from laws against blacks attending white schools, to anti-miscegenation laws, to anti-gay laws. So they feel that they have to demand that the government put laws in place to prevent such abuses in the future, which makes sense.
Many feminists seem to want the government to play the role of sort of a husband-surrogate, something to turn to in times of need while eliminating their having to deal with that annoying... man.
Never met a feminist like that. Perhaps you hang out with a different group than I do.
Right wingers tend to want the government to protect them from more imagined evils - Muslim terrorists from certain countries, the "gay agenda," the evil EPA that is destroying their business. Right wing politicians know that they are more fearful than average, and they use this to their advantage, playing up the threat of foreigners or the threat of man-hating feminists to garner their support.
Conservatives want their government benefits, but at the same time they want smaller government. It's always interesting to see what happens when a conservative is confronted with this dilemma. From an article in 2010:
========
Some [conservatives] defended being on Social Security while fighting big government by saying that since they had paid into the system, they deserved the benefits.
Others could not explain the contradiction.
“That’s a conundrum, isn’t it?” asked Jodine White, 62, of Rocklin, Calif. “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.”
========
Lately they have also started to become anti-science. Science occasionally conflicts with religion, and they feel they have to choose one or the other. So they choose creationism over evolution, denial over climate change science and anti-vaxxing over medical science. This is reinforced when they "choose a side" and science tends to weaken their side of the argument, as it does with climate change and carbon emissions. This is one reason that IQ and educational status has become a better and better predictor of political party affiliation.