In the ongoing battle of the budget, President Obama has done something very cruel. Declaring that this time he won’t negotiate with himself, he has refused to lay out a proposal reflecting what he thinks Republicans want. Instead, he has demanded that Republicans themselves say, explicitly, what they want. And guess what: They can’t or won’t do it.

No, really. While there has been a lot of bluster from the G.O.P. about how we should reduce the deficit with spending cuts, not tax increases, no leading figures on the Republican side have been able or willing to specify what, exactly, they want to cut.

And there’s a reason for this reticence. The fact is that Republican posturing on the deficit has always been a con game, a play on the innumeracy of voters and reporters. Now Mr. Obama has demanded that the G.O.P. put up or shut up — and the response is an aggrieved mumble.

Here’s where we are right now: As his opening bid in negotiations, Mr. Obama has proposed raising about $1.6 trillion in additional revenue over the next decade, with the majority coming from letting the high-end Bush tax cuts expire and the rest from measures to limit tax deductions. He would also cut spending by about $400 billion, through such measures as giving Medicare the ability to bargain for lower drug prices.

When you put Republicans on the spot and demand specifics about how they’re going to make good on their posturing about spending and deficits, they come up empty. There’s no there there.

Republicans have howled in outrage. Senator Orrin Hatch, delivering the G.O.P. reply to the president’s weekly address, denounced the offer as a case of “bait and switch,” bearing no relationship to what Mr. Obama ran on in the election. In fact, however, the offer is more or less the same as Mr. Obama’s original 2013 budget proposal and also closely tracks his campaign literature.

So what are Republicans offering as an alternative? They say they want to rely mainly on spending cuts instead. Which spending cuts? Ah, that’s a mystery. In fact, until late last week, as far as I can tell, no leading Republican had been willing to say anything specific at all about how spending should be cut.

The veil lifted a bit when Senator Mitch McConnell, in an interview with The Wall Street Journal, finally mentioned a few things — raising the Medicare eligibility age, increasing Medicare premiums for high-income beneficiaries and changing the inflation adjustment for Social Security. But it’s not clear whether these represent an official negotiating position — and in any case, the arithmetic just doesn’t work.

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Start with raising the Medicare age. This is, as I’ve argued in the past, a terrible policy idea. But even aside from that, it’s just not a big money saver, largely because 65- and 66-year-olds have much lower health costs than the average Medicare recipient. When the Congressional Budget Office analyzed the likely fiscal effects of a rise in the eligibility age, it found that it would save only $113 billion over the next decade and have little effect on the longer-run trajectory of Medicare costs.

Increasing premiums for the affluent would yield even less; a 2010 study by the budget office put the 10-year savings at only about $20 billion.

Changing the inflation adjustment for Social Security would save a bit more — by my estimate, about $185 billion over the next decade. But put it all together, and the things Mr. McConnell was talking about would amount to only a bit over $300 billion in budget savings — a fifth of what Mr. Obama proposes in revenue gains.

The point is that when you put Republicans on the spot and demand specifics about how they’re going to make good on their posturing about spending and deficits, they come up empty. There’s no there there.

And there never was. Republicans claim to be for much smaller government, but as a political matter they have always attacked government spending in the abstract, never coming clean with voters about the reality that big cuts in government spending can happen only if we sharply curtail very popular programs. In fact, less than a month ago the Romney/Ryan campaign was attacking Mr. Obama for, yes, cutting Medicare.

Now Republicans find themselves boxed in. With taxes scheduled to rise on Jan. 1 in the absence of an agreement, they can’t play their usual game of just saying no to tax increases and pretending that they have a deficit reduction plan. And the president, by refusing to help them out by proposing G.O.P.-friendly spending cuts, has deprived them of political cover. If Republicans really want to slash popular programs, they will have to propose those cuts themselves.

So while the fiscal cliff — still a bad name for the looming austerity bomb, but I guess we’re stuck with it — is a bad thing from an economic point of view, it has had at least one salutary political effect. For it has finally laid bare the con that has always been at the core of the G.O.P.’s political strategy.