The fact I do not "trust" the government does not mean I question the necessity of its existence.
In the 1990's, Congress "Fixed" Social Security by placing the funds from your FICA taxes in a "Lock Box." This let everyone feel nice and safe, and believe that Social Security would exist for them 25, 30, or even 50+ years later. However, those paying attention at the time knew there was no "Lock Box." There was a special account, as such things go in Washington, but all funds were going first to the general fund, and then IOUs were being placed "in the account" for Social Security instead of actual money.
It is this kind of obfuscation of the facts that make conservatives distrustful of government. We do not believe that government is not necessary. We do not believe in anarchy (indeed: most anarchists are socially very liberal). We do believe that "power corrupts and absolute power corrupts absolutely." We believe that man's fallen nature makes him predisposed to do things for his own benefit with little or no regard for the harm it causes others.
That is why we advocate for smaller government. A government which is relatively small and weak is a government with less power to enrich itself at the cost of the citizenry. A limited government is one that has less (ideally: no) power to "pick winners and losers," or skew the marketplace. A limited government is one that cannot lie to the people, because it is governed by them as much as they are governed by it.
This is also why we advocate for Federalism. A fragmented government, not just among three branches, but also among several levels, is easier to keep in check. A citizen, just trying to live his life, often doesn't have the time or inclination to keep an ever-watchful eye on Washington DC, their State capitol, and their local city hall. So, with true federalism, and strong States, this responsibility is cut by a third. We still have to mind both our local and our State governments, but the State government then becomes a check on the Federal government- and the semi-antagonistic nature that is inherent in 50 (or even 13) states each preventing the others from getting some "unfair" advantage makes it relatively easy for a citizen simply to check occasionally.