Far-right Republicans are winning the budget wars because they understand something that nobody else in Washington seems to grasp: The old truism about politics being the art of the possible is no longer true.

There’s no question who won last week’s showdown. The outcome — nearly $40 billion in painful cuts — goes well beyond the GOP’s initial demands. That Democrats were able to save a few pet programs is something, but not much. You really don’t need a weatherman to know which way the wind is blowing.

And as anyone who’s paying attention can plainly see, The Great Shutdown Standoff was just a skirmish in a much bigger conflict. At issue is a fundamental question — What is the nature and purpose of government? — that was first answered more than two centuries ago, when Alexander Hamilton and Thomas Jefferson duked it out as warring members of George Washington’s first Cabinet. Hamilton’s centralized government was victorious. There are those who have never forgiven him.

The far-right ideologues in the House seek to starve the federal government to the point where it can no longer fulfill its constitutional duty to promote the general welfare. I don’t mean to sound apocalyptic, but that’s what this struggle comes down to.

Their inspired tactic — which has worked so well that they would be crazy to abandon it — has been to take a wildly extreme position and stick to it with the obstinacy of a mule. When Democrats offer to negotiate, Republicans increase their demands. The result is that they shift the battlefield and end up fighting on terrain so friendly that they literally can’t lose.

So an initial GOP call for $32 billion in cuts was raised to $61 billion — a ridiculously impossible number. Of course they didn’t get it — but they got almost two-thirds of the way there.

Democrats, including President Obama, continue to play by the old art-of-the-possible rules. Bless their hearts. They caucus, they cogitate, they ruminate, they make reasonable concessions and ultimately come up with a result that everyone, surely, should be able to live with. Then they get hit with the next sucker punch.

Obama, I fear, is about to repeat the pattern.

The road map for debt reduction and entitlement reform that Rep. Paul Ryan, R-Wis., the GOP’s designated philosopher, has put on the table is a radical proposal. It would cut taxes for the wealthy, worsen the struggles of the beleaguered middle class and alter Medicare and Medicaid to the point where they would be unrecognizable. Ryan seeks not just to reduce the nation’s long-term indebtedness but to change the essence of the relationship between citizens and their government.

Ryan pays lip service to the need to maintain and strengthen America’s safety net, but nothing in his plan suggests he really believes in the idea of collective responsibility for those in need. His favorite author, the laissez-faire extremist Ayn Rand, would be proud.

Progressives who do believe that a healthy, prosperous nation is more than a collection of self-interested individuals have a duty to respond. From all indications, the plan for debt reduction and entitlement reform that Obama plans to announce Wednesday will include a mix of sensible spending cuts and modest tax increases — something that everyone should be able to live with.

But mark my words, the response from the ideologues of the far right won’t be to sit down with the president and negotiate a middle course. They won’t even pretend to look for common ground. They’ll insist on spending cuts in the 2012 budget that go far beyond even the outrageous demands that Republicans made for the current year. As leverage, they’ll have a crucial upcoming vote on raising the debt ceiling to avoid a catastrophic default. Think they won’t try to use it?

Politically, Obama gets to be seen as sensible, pragmatic, and more interested in solutions than political gamesmanship. But step back and look at the bigger picture. Why are we even talking about spending cuts, rather than increases, when the economy is still struggling to climb out of one of history’s worst recessions? If rising medical costs are the real long-term problem, Obama’s reform law took the first steps toward a solution. Why aren’t Democrats saying the obvious: We need to go farther down that road — at least to a government health plan — rather than reverse direction.

Crazy talk? Maybe. But Republicans are proving that demanding the impossible is an excellent place to start.

Eugene Robinson’s e-mail address is eugenerobinson(at)washpost.com.