In Barbara Tuchman’s classic account of the outbreak of World War I, “The Guns of August,” neither Germany nor its adversaries seem to want war in 1914. But they stumble into it anyway. Substitute “default” for “war” and you have a good idea of where we are in the Great Debt-Limit Crisis of 2011.

After talking to sources in the White House and on Capitol Hill this week, I think I have a good idea of how this should play out -- in a rational world.

Republicans have believed all along that President Barack Obama can be played, rolled, humiliated and forced to fully capitulate. More than a few have extended that belief to the Senate: I’m told that emissaries of the Republican leadership assured business executives all week that Democrats in the Senate would fold and approve House Speaker John Boehner’s plan after it passed the House.

This belief was naive. First, Boehner is having much more trouble convincing House Republicans to go along with his plan than expected. And Democrats have their own ideas anyway.

So we’re likely to have a weekend of negotiations between Senate Minority Leader Mitch McConnell and Senate Majority Leader Harry Reid, who has proposed his own plan for raising the debt limit. The two men don’t like each other but have done deals for years.

In a rational world, the compromise they fashion would go back to the House next week and be approved, with the votes of 90 Democrats replacing those of the Tea Party Republicans who hate Boehner’s plan. Then Obama would sign the bill early next week, and the crisis would end.

The reason this remains a plausible outcome is that the differences between the Reid and Boehner bills are relatively small. When they are reconciled over the weekend -- and attached to an amended version of the cynical but shrewd legislative procedure that McConnell has suggested -- we should have a deal.

The two bills reduce budget deficits and cap discretionary spending by about the same amount. Reid’s proposal actually cuts deficits more because it relies on savings from winding down the wars in Iraq and Afghanistan.

Neither bill includes real revenue increases, a clear victory for Republicans, though a hollow one, considering that taxes will almost certainly go up in 2013 when the Bush tax cuts expire. Neither bill offers much detail about cuts -- that’s the way politicians do it -- or convincingly binds future Congresses.

The big difference is in how each plan deals with future votes on the debt ceiling. Republicans want to hold the system hostage again next January. Democrats want this issue settled through the 2012 election so they can start talking about something else for a change.

This is where the markets come in, and in a way that helps the Republicans. The news that Standard & Poor’s is considering a downgrade of the U.S. government’s AAA credit rating is increasing pressure for future deficit reductions.

Obama is willing to accept trigger mechanisms to cut deficits, but he and Reid don’t want reductions down the road (whether through a new “Super Congress,” as proposed by Boehner, or even a revived “Gang of Six” process) to be tied to raising the debt ceiling. Their bottom line is to decouple triggers from debt ceilings and avoid another hostage-taking episode in six months.

The rational way around this is to adopt McConnell’s convoluted plan of giving the president the power (and attendant blame) for raising the debt ceiling in increments over the next year. In brief, McConnell’s maneuver would allow the debt limit to be raised, but without Republicans having to vote for it.

This plan is obviously the old Washington way of doing things, but it sure beats default and downgrade.

The big question is whether Boehner reacts by telling his caucus, “Hey, we got 85 percent of what we had in my bill!” or feels so much Tea Party pressure that he goes further to the brink next week.

With any kind of deal, Obama is going to have a hard time explaining how he didn’t get his clock cleaned. Republicans prevailed in keeping taxes out, and they won on cutting spending by about as much as the debt ceiling will be raised. In a rational world, that would constitute victory.

But maybe it’s 1914. Maybe the British and the Germans are misjudging each other’s cables, while troops mass on the French border.

(Jonathan Alter, the author of “The Defining Moment: FDR’s Hundred Days and the Triumph of Hope,” is a Bloomberg View columnist. The opinions expressed are his own.)

To contact the author of this column: Jonathan Alter at alterjonathan@gmail.com.

To contact the editor responsible for this column: Timothy Lavin at tlavin1@bloomberg.net.