Richard Nixon espoused what he called "the madman theory." It's a negotiating approach that induces the other side to believe you are capable of dangerously irrational actions and leads it to back down to avoid the wreckage your rage might let loose.

House Republicans are pursuing their own madman theory in budget negotiations, with a clever twist: Speaker John Boehner is casting himself as the reasonable man fully prepared to reach a deal to avoid a government shutdown. But he also has to satisfy a band of "wild-eyed bomb-throwing freshmen," as he characterized new House members in a Wall Street Journal interview last week by way of comparing them fondly to his younger self.

Thus are negotiators for President Obama and Senate Democrats forced to deal not only with Republican leaders in the room but also with a menacing specter outside its confines. As "responsible" public officials, Democrats are asked to make additional concessions just to keep the bomb-throwers at bay.

This is the perverse genius of what the House Republicans are up to: Nobody really thinks that anything like their $57 billion in remaining proposed budget cuts can pass. It's unlikely that all of their own members are confident about all of the cuts they have voted for. But by taking such a large collection of programs hostage, the GOP can be quite certain to win many more fights than it would if each reduction were considered separately.

Begin with the outrageous $1.1 billion, 15 percent cut from Head Start, a program that offers preschool education to roughly 965,000 poor children. According to the Center for Law and Social Policy, this would knock 218,000 kids out of Head Start and force 16,000 classrooms to close.

That is an excellent way to lose the future, as Obama ought to be saying. What could be a better use of public money than helping our poorest children early in life so they might achieve more in school, and later?

And for those who say that Head Start is not as good as it should be, the administration announced plans in September to require lower-performing Head Start programs to compete against other entities for continued funding. Isn't this the sort of competition conservatives say they're for?

Given what science has shown about the importance of a child's first years, we need better and broader early childhood programs. Slashing them can only cause harm - to parents, to children and to the country.

Then there are the cuts at the other end of the education continuum. The House budget would reduce the maximum Pell Grant, which helps needy kids go to college, by $845, from $5,550 available now. According to Mark Kantrowitz, who publishes the FinAid Web site that gives financial-aid advice, 1.7 million low-income students would lose eligibility for Pell Grants, almost a fifth of current recipients. Is that what Americans voted for last November?

But here is where the Republicans' strategy works so brilliantly. Let's assume that neither the administration nor Senate Democrats - even the most timid among them - can allow the Head Start or Pell Grant cuts to go through. That still leaves a lot of other truly worthy programs to be defended. By heaping cut upon cut, Republicans get advocates of each particular cause fighting among themselves.

And with so many reductions on the table, voters who would actually oppose most of them if they knew the details don't get to hear much about any individual item because the media concentrate almost entirely on the partisan drama of the shutdown fight, not the particulars.

You can also imagine the argument from those Democrats petrified of their own shadows. "Well," say the scaredy-cats, "we have to save Pell Grants and Head Start, so why don't we give House Republicans what they want on the National Endowment for the Arts - or their cuts in foreign aid, the Centers for Disease Control and Prevention, medical research, the Women Infants and Children program, meals-on-wheels or mine safety inspections? I mean, we have to give them something, or those crazies will shut down the government, and we might get blamed."

Boehner can just sit back and smile benignly as Democrats battle over which concessions they should give him. When the negotiating gets tough, he can sadly warn that his freshmen need more because he can't guarantee what they'll do. The perpetually tanned one is a shrewd dude. Democrats who underestimate him will be playing into his hands.

ejdionne@washpost.com