Normally I try to document my responses with a source substantiating them. In this case, however, you appear to be asking for an honest, civil opinion.
If I am correct, allow me to reply by stating, from my observation over the past 30 years or so, that the GOP uses "smaller government" as a code word. I do not believe that they really want smaller government; were that the case, they would have made it smaller when they controlled both Houses and the Presidency.
"Smaller government" is code for the least coverage possible of the poor, the elderly, the needy, and the infirm, and it means privatization of Medicare and Social Security. The term means terminating or reducing materially spending earmarked for the social safety net (like the Earned-Income Credit; tax credits to help lower-income parents pay for child care; Supplemental Security Income for the elderly or disabled poor; unemployment insurance; assistance for low-income families and individuals: food stamps, school meals, low-income housing assistance, child-care assistance, and assistance in meeting home energy bills; aid for abused and neglected children, etc Total assistance to the neediest Americans has been decreasing and is budgeted to continue to decrease; it comes to about 14?f the total budget..--see http://www.cbpp.org/cms/index.cfm?fa=view&id=1258
Defense, by way of contrast, comes to 20?the same amount spend on Social Security and Medicare combined) and it is expected to hold steady at this level over the next four years--see http://www.usgovernmentspending.com/welfare_budget_2011_4.html
Most of defense spending benefits private contractors, and many of these contracts awarded with no competition (remember the lavish Halliburton and Blackwater contracts?).
None of the figures accounts for tax spending in the form of tax cuts and credits from borrowed money and benefiting only the wealthiest individuals and corporations in this country. This tax spending, we are told, is sacrosanct and cannot be reduced; cuts must come from Medicare, Medicaid, and "entitlements" in general.
It sounds good to talk of reducing the size of government and cutting spending if one does not have to specify what part of government will be reduced and what spending will be cut. Note that GOP spokesmen always phrase their replies to questions about specific programs by brushing off discussion about the programs themselves and by talking instead about tax increases in general (to give the misleading impression that the increases would be imposed on everyone, not just on the wealthiest people in our society, those who do not reinvest their wealth to create new enterprises, new hiring, and new jobs (remember trickle-down, supply-side prosperity that would be the tide lifting all boats?).
They do the same with spending; they do not speak of what spending they would cut--the impression left is that they will cut only wasteful spending (which, to many non-Jewish whites means "handouts" to minorities, whom whites blame for intrusions on the societal order that these whites recall as having benefited them before the blacks, Hispanics, and feminists "took over").
Answering your question, the Republicans are expanding the government because expansion is required to meet the ever-growing demands of their powerful, wealthy benefactors whose thirst for more corporate welfare can never be slaked. If a Republican (or Democrat) indebted to these special interests were to do no more that to say, "Let's hold the line on spending earmarked for the corporatocracy," he/she would see his political career cut short.