Washington ? Rivals in a divided government, President Barack Obama and the most powerful Republican in Congress split their differences to stave off a federal shutdown that neither combatant was willing to risk.

Their compromise is the result of a battle pitting the enduring power of the presidential veto and the White House soapbox — despite a “shellacking” in the last election — against a strong-willed GOP House speaker vaulted into office by a voter revolt against Washington’s free-spending ways.

The resulting measure will bleed about $40 billion from the day-to-day budgets of domestic agencies over just the next six months, the biggest rollback of such government programs in history. It allows Speaker John Boehner, R-Ohio, to claim his GOP shock troops had put Cabinet department operating budgets on track toward levels in place before Obama took office. In the end, the White House had to meet Boehner more than halfway on spending.

On the other side was a strong-willed Obama, who mostly succeeded in forcing Republicans to cave in on dozens of controversial conservative policy prescriptions — including rolling back environmental protections and cutting off Planned Parenthood from taxpayer assistance while protecting favored programs like education, clean energy and medical research.

It was, in short, the type of split-the-differences deal that a political scientist might have predicted from the start, given the realities of divided government.

Obama stood firm against GOP attempts to block the Environmental Protection Agency’s ability to issue global warming rules and other reversals of environmental regulations. Obama’s wins on the environment were matched by a bitter battle in which he said no way to GOP demands to cut off Planned Parenthood from federal help. The results, taken together, pleased core Democratic constituencies of environmentalists and women.

But it’s clearly a win for Boehner, who despite accepting billions of dollars in questionable savings demanded by Democrats as a substitute for cuts in domestic programs, ended up basically where he started in the first place. The original plan backed by Boehner in February called for cuts in the range of $35 billion as a campaign promise down payment that reflected the fact that the budget year was half over.

But conservative Republicans, many elected with tea-party backing, demanded far bigger cuts of more than $60 billion that would have led to widespread furloughs and harm to programs like food inspection, tax collection and U.S. overseas diplomatic efforts. The final deal, a product of weeks of wrangling, got Republicans back to their original goal, while avoiding most of the harsher effects of the tea party-backed version.

“We’re not going to roll over and sell out the American people like it’s been done time and time again here in Washington,” Boehner said Friday, hours before the agreement came together. “When we say we’re serious about cutting spending, we’re damn serious about it.”