Republicans are convinced they have a mandate to cut government down to size. That’s hard to do when you only control one House of Congress, and harder still when your fiscal plans are fraught with internal contradictions.

It’s not even clear, for instance, what Republicans really want to accomplish. Senator-elect Kelly Ayotte, delivering the GOP’s weekly address Jan. 1, said that “Job one is to stop wasteful Washington spending.” At the same time, she said that “Congress must get serious about meaningful debt reduction.”

So which is it—cut public spending or cut public deficits? That’s a distinction with a difference, especially to investors worried about the basic soundness of the U.S. economy. To them, deficits are simply the arithmetic result of government spending too much, taxing too little or both, as is clearly the case today. Last month, Republicans struck a deal with President Obama on a tax cut package that will add $950 billion to the nation’s debts. Key GOP House leaders have made it clear they will oppose any tax hikes to solve the budget crisis, which they pretend is purely a matter of overspending.

Ayotte seemed closer to the mark in saying Republicans come to Washington to “make government smaller, not bigger.” In practice, however, that ideological goal may not be compatible with what the public seems to want. Independent voters especially have focused on narrowing the enormous deficits that force America to get deeper and deeper in hock to Chinese and other foreign lenders.

And if Republicans are serious about taking taxes off the table, they’ll have to make even deeper cuts in public spending—including Social Security, Medicare and Medicaid—to close our yawning budget gaps. It will be interesting to see which GOP bravos are willing to walk that plank. Thus far, House Republicans are proposing only cosmetic cuts, like trimming the House budget by $25 million. It’s a good idea for the House to discipline its own spending, but in a $3 trillion budget, that’s chump change.

Meanwhile, the GOP is planning to vitiate budget caps imposed by the previous Congress. Under the caps, any new spending or tax cuts would have to be offset by equivalent spending cuts or tax hikes. Republicans would eliminate the later requirement, so that tax cuts too would trigger deeper spending cuts. This of course is a formula for a deepening fiscal crisis and intensifying polarization between the two parties. And House Republicans will take a run at repealing Obamacare, which would certainly reduce federal spending but actually increase future budget gaps. In any event, it’s not happening

Some of the more fervid Tea Party types are even threatening to vote against raising the debt ceiling in March if Democrats don’t agree to new spending cuts. If they are serious, this could mean America would default on its debts for the first time in history. It would be, as Obama’s chief economic adviser, Austan Goolsbee, said yesterday, an act of political insanity, the equivalent of taking yourself hostage and threatening to shoot.

Finally, there’s the crucial question of timing. Incoming House Budget Committee Chairman Paul Ryan reportedly is planning a package or rescissions aimed at cutting about 21 percent from 2011 spending Congress approved last year. The aim is to return domestic spending to its 2008 level, before Obama took office.

The risk is that withdrawing a significant chunk of fiscal stimulus could abort an economic recovery that at last seems to be getting traction. There’s no question that Americans want to restore fiscal discipline in Washington, but what they want even more is for the economy to grow and unemployment to start falling.

Goolsbee hinted that Obama’s next budget also will contain some spending cuts. But the GOP’s ideological zeal to cut government gives Obama an opportunity to offer a more pragmatic approach that puts jobs growth first, while taking balanced and gradual steps to put the federal government on a fiscally sustainable course.

Progressives do need to get serious about getting federal spending under control. But by framing the coming fiscal battles as a choice between a more robust economy and a smaller government, they can speak directly to Americans’ number one priority and thereby regain the political initiative.