When President Obama abruptly ended Wednesday’s round of deficit negotiations, it wasn’t because the Republicans had demanded cuts he couldn’t accept or a dollar figure he considered too high or too low. It was because Majority Leader Eric Cantor (R-Va.) pushed — repeatedly, in the White House’s telling — for a schedule the administration had already ruled out.

All the attention is on the size and composition of the debt-ceiling deal. But the cuts are proving less troublesome than the calendar. The timing of a deal — or, if the Republicans have their way, the deals — is playing an increasingly significant role in the two parties’ strategies.

The White House has come to the conclusion that its interests are best served if there’s one deal and if it wraps up before the election. Republicans, meanwhile, see an advantage in forcing a series of smaller deals, both before and after the election.

Both sides are probably right.

If there’s only one deal, it means the final number is $4 trillion or more. You can’t do that in one shot without tax increases. So that’s the GOP’s first concern: If they do this all at once, they’ll have to give on revenues.

If they do this in pieces, how­ever, there’s reason to think they won’t have to give on taxes — or at least will have to give less. The Obama administration has signaled that it could accept a debt-ceiling deal in the range of $1.5 trillion to $2 trillion that’s all spending cuts. If the two parties strike that agreement, they’ll have to come back, either before or after the election, and go for another $2 trillion or so. If Republicans hold that deal to 3-to-1 spending cuts to tax increases, then all together, the deficit deal would be 7-to-1 spending cuts to tax increases. Neat trick, huh?

The hitch in this plan should be the Bush tax cuts. They expire at the end of 2012. All Obama has to do to raise taxes is veto efforts to extend the Bush cuts. He’s got all the leverage in that debate. But what’s become increasingly clear is that he doesn’t want to veto the Bush tax cuts. He’d much prefer a negotiated solution to a hostage situation.

So if you’re a Republican, the multi-deal scenario leaves you with two futures: Either Obama loses the election and you’re bargaining with a Republican president, or he wins and you cut a second deal that raises taxes by some very small amount. Either way, you end up with less in taxes than if you do in one big deal.

A single deal also has political disadvantages for Republicans. It takes the deficit issue off the table in the coming elections. It revitalizes Obama’s brand as a post-partisan leader who can bring the two sides together. It ends the deficit conversation, where Republicans are strong, and clears the deck for the administration to focus on issues where it and its position will be more popular, such as infrastructure and education.

All these disadvantages are, of course, advantages for the White House. And there are a few more: A big deal could include more stimulus, perhaps an extension of unemployment insurance and the payroll tax cut. It also makes it easier to push the cuts back a couple of years, when the economy will, in theory, be stronger.

This has led to some peculiar negotiating dynamics: The Obama administration, which many people considered cool toward a deficit deal, has been willing to concede much more than anyone expected — including raising the Medicare eligibility age and cutting Social Security. Republicans, who made the deficit their top priority in the last election, have been willing to concede much less. But the difference isn’t really that the Obama administration wants a deal and Republicans don’t. It’s that the Obama administration wants to reach a big deal now and the Republicans want a series of smaller deals dragged out over as long a period as is politically and economically feasible.