Historically, neither the GOP or Democrats have proven themselves to be the party of small government ]
Historically, the GOP was the party that said 'big government makes things worse'. When we want to help the poor, we cripple them with government dependency. When we want to help the economy, we distort it and make it worse. When we want to help education, we end up lowering standards. When we want to help with health care, we make that worse.
The GOP, properly understood, was the party that said the way to make things better is by having the federal government do the big things it does well, things only it can do, the military, infrastructure, regulation as referee, not as deciding winners and losers and stay out of everything else. That's the way the Constitution was set up. That's sound ideological thinking in terms of human behavior and, of nothing else, it's the proper course of action if we merely look at the enormous failures of progressive/socialist policies when implemented.
Public housing. Welfare as hand out instead of helping hand. The aforementioned problems with healthcare and education. On and on and on. MOST issues will be made worse by federal government involvement. We know that intellectually and factually. Hell, even things like Sandy and Katrina were worse than need be BECAUSE, over the years, there was the sense that in fact and in understanding, same as Wall Street, ultimately, the federal government will make poor decisions it help encourage everyones problem.
So, send me to Vegas. Heads I win, tails, you lose.
In any event, ALL of that became crystallized in 1994 when the GOP, for the first time in FORTY years, 20 congressional election cycles, took over the House of Representatives, the house of the purse strings.
Finally! A chance to effect some real changes AT the funding level! And things went fairly well with Clinton and a GOP House.
Then, in 2001, the whole ball of wax, House, Senate, White House, plus a favorable court. Never mind ideology, here was THE chance to act, to walk the walk. To reign in entitlements. To cut wasteful, hurtful programs. To bring market competition to health care and education. To relieve industry and states of the weight and waste of unfunded mandates. To get government back within the constraints of the Constitution.
And look what happened.
So, the GOP was the party of limited government...when they had no power to make it so.
It is impossible to understate the damage done under George W. Bush be it expanding entitlements with Med Part D or No Child Left behind (more federal intervention in education) or ignoring the coming housing crisis HE warned was coming in April of '01 or the massive over reaction to 9/11, DHS, TSA, The Patriot Act (which, with a name like that is a lot like selling 'Clean' poo) the conduct of the wars as social experiments instead of war winning. A GOP president actually bailing out the UAW and then the piece de resistance, TARP.
Ultimately, you are correct; the GOP is NOT a small government party. Not when it matters. But, we had a chance. We had a shot. And the American people put us in charge of the House in '94 and the Senate and White House in '01 SPECIFICALLY to reign in government. And look what we did. We can't name ONE thing past tax cuts we did, when we had the chance, that would remotely be considered small government or conservative.
People like Chris Christie, McCain, etc, are not Republicans in name only. They ARE Republicans.