If President Obama honestly wants to negotiate an agreement with Republicans before the year-end fiscal deadline, he must be deeply frustrated. And if he doesn’t really want to negotiate with them, then he should be delighted, for the same reason: Their latest “offer” laid before him by House Speaker John Boehner demonstrates again their refusal to reveal their true intentions — and their inability to do simple arithmetic.

Consider their treatment of Medicare, the popular social insurance program for seniors that Republicans have always despised. They have just emerged from a long national campaign in which they repeatedly and falsely claimed to “protect” Medicare from the president — whom they accused of wanting to slash $716 billion from the program — but now they complain that he won’t cut it enough. The Obama cuts were mythical, but the Boehner budget proposal includes at least $600 billion in Medicare and Medicaid reductions.

Worse still, the Republicans propose to perform this crude surgery on Medicare without the slightest explanation of where they would cut. Washington rumors suggest that they would achieve some of those cuts over the next 10 years by raising the eligibility age by two years to 67 and by increasing premiums for more affluent beneficiaries.

As Robert Greenstein of the Center on Budget and Policy Priorities pointed out on Tuesday, however, those changes would not begin to achieve the savings required by the Boehner proposal.

The same problem undermines the other aspects of Boehner’s proposal, which includes $600 billion in additional unspecified cuts. Either their arithmetic doesn’t work — or, as Greenstein worries, they mean to inflict severe cuts in health and other services that would harm elderly and poor Americans, but want to conceal those consequences from the public.

Yet there is an even deeper problem with Boehner’s arithmetic. The Republicans are fighting to extend all the Bush tax cuts to the wealthiest two percent along with everyone else — but their alternative proposals are utterly inadequate to compensate for the $1.3 trillion in revenues lost by continuing those cuts for the rich. To “offer” $800 billion in new “revenues” obtained by eliminating deductions rather than raising rates simply doesn’t work, as a matter of basic math. It isn’t nearly enough money.

If Republican leaders cannot do the arithmetic, then it is impossible to negotiate with them. If they can do the arithmetic but insist on falsifying the answers, then it is both unwise and impossible to negotiate with them.

Unless and until the Republicans start talking about real numbers that can actually add up, there is nothing to be gained from pretending to negotiate. Nor should the president start negotiating with himself, as he has sometimes done in the past. Instead, he ought to make sure that the opposition understands what will happen when they fail to act responsibly. After Jan. 1, he will bring them an offer they cannot refuse to restore cuts for the 98 percent — and they will be held accountable for any consequences caused in the meantime by their stalling.