DHS is a problem but it is not the problem. It's a symptom of the problem of excessive government control over our lives. For the most part the DHS is just an amalgam of other agencies anyway, and those would still exist even if the DHS did not.
Excessive government control is not exactly the same as big government. IOW, you can be against too much control (i.e. massive spying on innocent citizens) and still want public healthcare and so on.
In theory, sure, in practice I don't think it's ever worked out that way. Can you give examples of countries with sizable government expenditures (e.g. 40% GDP or more) that do not also feature onerous regulation and extensive government interference over many aspects of daily life?
I can't give examples without that expenditures either. To be honest, I don't know which countries are on either side of that boundary, but countries that are usually put in the big state bag, like scandinavian ones, are not specially known for much state interference.
BTW, I would only consider first world democracies. Others' problems are arguably caused by different, more obvious, factors.
