For accounting purposes, it makes sense to count programs like Social Security, disability insurance, and Temporary Assistance for Needy Families as government spending. But these kinds of programs are not really government spending because the government does not actually direct how the money is spent. Unlike building a road, for instance, where the government decides that a road should be built and then pays to make it happen, cash benefit programs involve the government distributing money to people and allowing them to decide where to spend it.
This is an important distinction because many of the problems people often raise about government spending simply do not apply to cash benefit programs. For example, one common criticism of government spending is that the government is incapable of figuring out what people actually want, and therefore wastes a bunch of money on projects and services that do not deliver much value. Another common criticism is that directly spending money generates all sorts of corruption and waste in the government contracting process. Big firms with lots of money competing for government contracts is a recipe for disaster due to the money-infused nature of our political system.
But these criticisms fall apart when we are talking about "spending" on cash benefit programs. The government is not having to guess at what will deliver value to people: the people who receive the benefits and do the actual spending can decide for themselves what is valuable. Additionally, the government does not have to contract firms to build things and provide services (except perhaps to administer the cash benefit program), which eliminates the contracting corruption problems.
Because the government is not actually spending the money, the only real spending in cash benefit programs is the money spent on program administration. But these costs are tiny up against the full sum of money being distributed. For instance, the Social Security Administration only spent 0.8% of its total expenditures on administering the program in 2012. Outside of these minor administrative costs, it is conceptually confused to call any of the other money involved in these programs "government spending." It is individuals spending money, not the government.
Given this, you'd think that the right-wing would be the least concerned about cash benefits programs if they were actually worried about government spending. These programs are much less wasteful than the kinds of direct government spending that the right is very favorable towards, e.g. purchasing bombs. That the right is the most concerned about cash benefit programs tells you a lot about where they are actually coming from in this debate. Although they talk about their dislike for "government spending," what they are really objecting to is a particular economic distribution.
Cash benefit programs are simply distributive institutions: they, along with our other economic institutions, determine which individuals get to spend money and how much. The government does not spend money on a cash benefit program, it just channels it to someone who spends it. The only coherent objection that can be raised against such a program is that the people the money is channeled to should not be entitled to spend it, that the money should actually be spent by other people. But this is a purely distributive argument. It is not a government spending argument, not even slightly. We should treat objections to cash benefit programs for what they actually are: complaints about the economic distribution that those programs usher in, not complaints about government spending.
Doing so will allow us to get at the real argument that is going on beneath the surface, which is the argument about who deserves what and why. If the right-wing believes that the poor, disabled, and elderly deserve to have less, then they should be forced to actually make that point overtly. I would love to see it too as I am especially interested in knowing just how much poorer the poor need to be in order for us to have a just economic distribution. But as it is, the actual disagreement about distributive justice never gets fought out. Instead, everyone involved fights a totally contrived proxy battle about government budgets that entirely obscures what's the debate is really about.