"The economy's bad, the president's party is being blamed, and Republicans are mad as hell." That, says University of New Hampshire polling expert Andrew Smith, is the reason the GOP scored quite so big this year. And even in a state like New Hampshire, which had seemed to be moving firmly to the left, an unexpected Republican clean sweep means big public spending cuts -- and promises to cut taxes as well.

In a host of states across the country, it's all about austerity: tackling state deficits and sweeping back a host of Democrat-inspired public programmes. Today, Republicans are in firm control of key battleground states like Ohio, Wisconsin, Michigan and Pennsylvania. In some cases, the switch in power was, the Washington Post says, "truly dramatic", like Texas, where one pundit has called the scale of the Democratic defeat "an annihilation bordering on political genocide".

And the pattern of Republican control is set to be entrenched for years to come. That's because they will now control the redrawing of congressional boundaries for the next ten years. Using today's sophisticated polling data, that means they can divide districts up extremely accurately, to best ensure a more solid Republican majority, while driving Democratic representation down.

The party also has the chance to show how they would act if they were in charge of the White House -- chiefly, how they'd tackle the economy.

In Florida, new Governor Rick Scott has pledged immediate tax cuts worth more than $2bn -- and in the long term he wants to axe the corporate income tax altogether. He's also vowed steep cuts in state spending, including pension savings, and a 5 per cent cut in Florida's public sector work force. Unions are already warning there could be trouble if cuts in areas like schools and healthcare are deemed to go "too far".

Indiana's new Republican leaders say they're determined to "live within their means", and have proposed slashing unemployment benefits. One cost-cutting idea in Pennsylvania involves selling off hundreds of state owned liquor stores, saving a couple of billion dollars, but axeing several thousand jobs in the process.

In Texas, Governor Rick Perry has suggested abandoning the state-funded Medicaid scheme and creating their own insurance programme for the poor. And Maine, which hasn't seen a Republican controlled administration for 60 years, is considering scaling back social security payments to focus on the "truly needy" -- while the state's own universal health care scheme is in for the chop.

It's not just austerity measures though -- the Republicans have won so big that in some cases they're putting conservative social legislation back on the agenda. The new governor of Kansas, Sam Brownback, could approve new limits on abortions proposed by the GOP-dominated state legislature. Stricter controls on immigration could now be introduced in New Mexico, while versions of Arizona's controversial immigration law may be on the cards across the south. South Carolina's incoming Governor Nikki Haley, couldn't be clearer: "I will tell you that if the Arizona style immigration reform comes to my desk, I will absolutely sign it.", she told a local paper.

So the battle lines are drawn. Now the GOP has a chance to show if they can really cut taxes, cut spending, and balance deficts -- for real, this time, not just as a campaign pledge. And all this, without cutting jobs and services so far, that they alienate those independent voters who swung their way in such overwhelming numbers.

The latest polls do indicate a mixed message for the Republicans. There's a desire for change, but not much appetite for other measures, like rolling back heathcare reforms, or social security -- especially among independents. So, from the economy to abortion rights, how the Republican-controlled state legislatures handle their new-found power will prove to be crtitical -- and is likely to determine the party's national fortunes, not just in 2012, but for years to come.

Felicity Spector is chief writer and US politics expert for Channel 4 News.