Based on historical record. The answer appears to be "no".

Figure 2 shows, in inflation-adjusted figures, how much each modern full-term president added to his predecessor’s final budget (or to his own, if he was re-elected). By this measurement, Republican George W. Bush outspent everyone. His apologists claim he had no choice but to expand military spending to combat terrorism at home and abroad. But even if you accept that argument, the president also increased domestic spending by massive amounts, including a giant new prescription-drug entitlement, the No Child Left Behind education law, and subsidy-soaked farm and transportation bills. Republican representatives and senators, many of whom were re-elected in 2010, share the blame for these measures: During the first half of 2001 and the 2003–07 period, the GOP maintained full control of both the White House and Congress.


and then there's this:

What about trade? According to Daniel Griswold, director of trade policy at the libertarian Cato Institute, “the incoming GOP House leaders, presumptive Speaker John Boehner of Ohio, Majority Leader Eric Cantor of Virginia, and Ways and Means Committee Chair David Camp of Michigan, have all voted more than two-thirds of the time for lower trade barriers.” But in his 2005 book Impostor: How George W. Bush Bankrupted America and Betrayed the Reagan Legacy (Doubleday), the former Treasury economist Bruce Bartlett makes a convincing case that Bush and the Bush-era Republican Congress were terrible on trade, pointing to their support for farm subsidies and import barriers that benefit politically influential groups such as sugar, rice, cotton, and corn producers.

It is even harder to claim that deregulation took place during the Bush years. Inflation-adjusted expenditures on regulatory agencies show a consistent upward movement for the last 10 years. While a popular narrative holds that the present economic crisis was preceded by a wave of financial deregulation, spending on finance and banking regulations rose by 26 percent during the Bush years.

In light of that track record, it’s hard to believe that the new Congress will seriously address our financial troubles. The next two years should give it ample opportunity to prove me wrong.

As has been repeatedly said, it's not that the Republicans won in 2010, it's that people believed that the Democrats would do and have done worse. In the tidal way of Republican domination at the state level, it is the Tea Partiers who have had the most overwhelming influence. I suspect most of those Americans have just as little faith as any of us - and that's why the face of the Republican Party is being changed by the Tea Partier, county executive by county executive. And that, is a good thing.