It’s always amazing how little Democrats and Republicans know about each other. Democrats, for example, are mystified that we haven’t already gotten a deal on the “fiscal cliff.” On Monday, the two sides seemed close. Both made serious counteroffers, and a deal seemed a day away.

Then Speaker John Boehner pulled back. He did this because senior Republicans were afraid that he was giving away the concessions they would need in a future tax-reform negotiation — like closing tax loopholes.

But Democrats don’t know this. They have no clue what Republicans are thinking at any moment. Republicans are equally in the dark. The White House is a black box to them. They have no clue what President Obama wants in his second term or how the fiscal-cliff negotiations fit in.

Well, I’d like to help the Republicans understand what’s going on in the other camp. First, Republicans should understand the mood in the White House. A month ago, the president and his team were gearing up for a fight. They were belligerent and tough-talking. Now, their mood is one of deep confidence. They’ve had a good month. The business community is on their side. Public opinion is breaking their way. Republicans are disorganized. The Obama folks project the self-assurance of a Duke basketball team warming up against a Division III school.

Second, Republicans should understand Obama’s incentive structure. He’s trying to map out his whole second term and write an Inaugural Address that will prefigure it. He wants to accomplish some big things: his middle-class economic agenda, immigration reform, a global warming agenda and government reform.

He cannot have a satisfying second term if the next four years look like the last two, with a string of debt-ceiling-type budget showdowns. If Obama’s going to govern the way he wants, he absolutely has to crush the Republicans on the debt-ceiling threat and on tax rates.

He’s going to be willing to fight tooth and nail to put the budget-showdown-era behind us. He simply has to win this. He’s going to be willing to go over the fiscal cliff and blame it on Republicans.

Given the weak Republican position, he’s going to conclude that his current offer is roughly the best he has to do. He’s just going to sit there, through hell and high water, and wait for Republicans to come to him. And since he’s sensitive to the liberal criticism that he’s a soft negotiator, he’ll love the chance to be implacable.

So over the whole span of his presidency, this is the moment when Obama is going to feel the least need to give ground.

But down the road, Obama does have a problem and, for Republicans, a vulnerability. Even if the cliff talks go his way, Obama will still face a money shortage. Entitlement costs are rising. Revenues can’t keep up. This squeezes the share of federal revenue that can be devoted to domestic discretionary programs — stuff like education, welfare, infrastructure, etc. As Eduardo Porter noted in an Economic Scene column in The Times, discretionary spending, which usually hovers around 3 percent or 4 percent of G.D.P., is scheduled to shrink to a paltry 1.7 percent in 10 years. That’s roughly the level envisioned in Representative Paul Ryan’s budget.

In other words, even if Obama gets a fiscal-cliff deal, he still needs to shake loose some money — either from the entitlement programs or from a new revenue stream — to pay for his programs. He is still caught in the remorseless vice that Christopher DeMuth describes in, “The Real Cliff,” a brilliant piece in The Weekly Standard. A generation of debt politics has left our leaders with no room to maneuver.

That means that in 2013, he will need to do comprehensive tax reform, find fresh revenue or take a broader whack at entitlements to shift some of that money to domestic programs.

As invulnerable as Obama is right now, he will be equally vulnerable next year to get these big projects done. The Republican strategy should be obvious. Swallow hard and accept a deal. End the showdown era. Achieve short-term fiscal stability. Don’t give away G.O.P. leverage on tax reform. Then focus on the bigger fight in 2013.

Don’t get hung up on some incremental tax increase for the rich. Instead, make sure America doesn’t have another credit downgrade. Make sure the economy doesn’t fall into another debt-exploding recession. Prepare a comprehensive tax and entitlement reform strategy for 2013. Call Obama’s bluff on health care reform. In case Obamacare doesn’t bend the cost curve, get Obama to agree to some automatic triggers — plans that will kick in and bring down health care spending.

A minority party has to learn how to pick its battles. The White House has a dominant position on the fiscal cliff and knows it. But next year Republicans can do big things.