ON THE budget, the daily shifts and convulsions within the Republican Party are more interesting and probably more important than the related feuding between the Republicans and Democrats. Rarely does it happen that an otherwise popular president is twice shot down by members of his own party on more or less the same major issue but from different directions in less than a week. But on the defining question of taxes, President Bush was first rebuffed last week by House Republicans when he proposed to zig, then coshed again the other day by Senate Republicans when he proposed to zag.

The party looks to be foundering, and in a sense it is. The elastic math of the past 10 years has finally caught up with it. No, you cannot cut taxes yet balance the budget if you are no more willing or able than the Democrats even to name, let alone subscribe to, the specific spending cuts that those contradictory goals require. But it's possible to argue -- we would -- that for the Republicans and the country generally this could be at least as much a liberating as a crippling set of events. The president seems to be trying to move himself and the party back from fiscal Disneyland to fiscal reality. The process isn't pretty, but that doesn't mean it is unhealthy.

The budget talks may also be in a healthier state than current rhetoric suggests, though here we are not so optimistic; the pattern in recent years has been to disappoint. The Democratic leaders also lost in the House last week. To create the kinder, gentler budget they think can pass, they have decided to ease the cuts that they and the president were supporting in Medicare and agriculture, abandon the ghoulish idea of limiting unemployment compensation on the eve of a recession and reduce the energy tax increases to which they had earlier agreed.

To finance this they suggested they would drop some business tax incentives on which the administration had earlier insisted and set up a front-loaded trade of a higher top income tax rate for a cut in the tax on capital gains. The higher rate would be felt well in advance of the gains cut.

That is the deal toward which the president seemed to be slipping at his news conference Tuesday morning -- he'd make the trade if there could be a "proper balance" between the increase and the cut -- and from which the Senate Republicans unceremoniously pulled him back Tuesday afternoon. No rate increase, they said.

But that doesn't take the talks all the way back to their starting point. The arguments now have to do not with whether to raise taxes or cut entitlements but with which taxes and which entitlements. A lot of steps that a few months ago were politically unthinkable have been legitimized by leaders on both sides, and both parties now have a political investment in deficit reduction that they did not before. There's still a chance.