Washington ? It’s hard to know which is more surprising: a Democratic president pushing historic cuts in spending, including Social Security and Medicare. Or a Republican-controlled House refusing to accept the deal and declare a huge victory for long-sought GOP goals.

Political orthodoxy has been turned on its head ever since President Barack Obama stepped up his call for a bipartisan “grand bargain” to raise the national debt ceiling and avert a default on U.S. obligations. The deal would include $4 trillion in deficit reduction over 10 years, mainly through steep spending cuts but also including up to $1 trillion in new federal revenue.

Those are far bigger targets than typical budget negotiations. And the spending cuts would seem more appropriate for a Republican president than a Democrat.

Some pundits and political insiders say Republicans should leap at the offer. But there’s a hitch: The new revenue — mainly from overhauling the tax code and lowering rates by eliminating or limiting a broad swath of loopholes, deductions and tax breaks — presumably would violate a no-net-tax-hike pledge that scores of Republican lawmakers have signed.

Mostly for that reason, House Republicans so far have rejected Obama’s overture, despite the interest shown by Speaker John Boehner. Some pro-Republican analysts seem bewildered.

Obama’s offer of big spending cuts would have “brutally fractured the Democratic Party,” and congressional Republicans probably “will come to regret this missed opportunity,” wrote David Brooks, a moderate-to-conservative columnist for The New York Times.

Such comments lead to a question: Why did Obama make the overture, and how might it affect him and his party as he ramps up his re-election campaign?

The consensus answer, based on interviews with key players in Congress, the White House and elsewhere, is that Obama may be maneuvering himself into a win-win political position for 2012, although it’s not without risks.

If Congress approves a version of the “grand bargain,” Obama can run next year as a president who began taming the runaway deficit, extracted concessions on higher taxes from Republicans and put Medicare and Social Security on a possible path toward greater stability.

If congressional Republicans block the plan — and especially if the Aug. 2 debt ceiling deadline is missed — Obama might persuasively argue that he tried his best to strike a compromise, at some political risk to himself. Recent polls suggest that strategy is working, as Americans seem disgruntled with the Republicans’ dug-in opposition.

Either way, Obama can appeal to the all-important independent voters next year, portraying himself as above the bitterly partisan House and Senate squabbles. Polls show that independents are deeply unhappy with Congress. Even if Obama’s ratings are not spectacular, he fares better.

A CBS-New York Times poll found that 68 percent of independents think an agreement on spending and the debt ceiling should include “a combination of both tax increases and spending cuts,” which is the president’s position. Fifty-five percent of Republicans in the survey hold that view.