It’s 65 days overdue and has been formally unveiled for less than an hour, but so far the Obama budget is being greeted with more bipartisan bewilderment than with genuine Republican anger or Democratic excitement.

And the nonplussed nature of the congressional response could be the best reaction possible for those who still hold out hope of achieving a grand bargain or, more precisely, for completing one. Things will stay muted for another couple of months, mainly to allow the gun control and immigration debates to play out but also because the next fiscal deadline is not until the middle of the summer, when Congress will need to raise the Treasury’s borrowing limit to avoid a default on government debt.

The consensus view of economists is that $4 trillion in collective red ink reduction in the next decade is what’s needed to take the deficit off the list of threats to long-term economic health. It’s also fair to agree that, with their various countdown clock showdowns and can kickings, the president and the Republicans have laid the foundation for achieving $2.5 trillion of that, in spite of themselves.

And the president’s budget would get safely beyond the rest of the way. His plan promises $1.8 trillion more in deficit reduction by 2024 — with $2 in the sort of savings that rankle Democrats for every $1 in the sort tax increases that infuriate Republicans — even while turning off the sequester’s across-the-board defense and domestic spending cuts this fall.

That ratio encapsulates how the president is not only challenging the GOP to reopen its acquiescence on taxes but is even more forcefully challenging Democrats to confront their entitlement addiction. And it’s genuinely meaningful that all of his Wednesday budget salesmanship outreach is aimed at Republican senators, a dozen of whom are headed to the White House for supper. (The full roster isn’t out but includes it Johnny Isakson, Orrin G. Hatch, John Thune, Michael B. Enzi, Susan Collins and Marco Rubio.)

What Obama is asking of the GOP on revenue is simply not as tough a political swallow for the party, especially in an off year, as what he’s asking of the Democrats on spending.

He would raise $580 billion entirely from the wealthy, requiring those with annual incomes above $1 million to pay at least 30 percent in income taxes (the “Buffett Rule”), limiting deductions on the top 2 percent of wage earners, ending the lower tax rate for investment fund managers and closing tax breaks for offshore accounts, corporate jets and businesses that send jobs abroad. He’s proposed all those things before, of course, but he hasn’t given up because of their palpable populist resonance.

But he’d reduce the pace of spending by almost twice as much, and in ways that he’s not really ever committed himself to in writing before, for fear of infuriating his own base: $400 billion by cutting Medicare payments to drug companies and other providers while requiring wealthier beneficiaries to pay more, $230 billion from adopting a different government inflation formula that would slow the growth of the Social Security cost-of-living adjustment and other benefits, $200 billion in cuts to farm subsidies and government pensions and $100 billion cuts each from military and domestic discretionary programs. (In other words, sticking with about one-sixth of the savings designed to come from the sequester.) The final $210 billion in savings would come from reduced debt payments thanks to reduced deficits

(The Obama budget is not only about cutting. It also proposes $50 billion to repair public works and less-expensive line items to support his ambitions for high-speed rail, universal preschool and innovations in manufacturing.)

Yes it’s true, as Republicans will point out, that many of the proposals for slowing spending will ramp up at the end of the budget’s 10-year time frame while the sequester’s forced march would be abandoned next year, so he’s essentially asking Congress to give up on certain savings now by promising alternative savings later. It’s also true that even in a decade there would be nothing close to balance, although by then the deficit would be only 1.7 percent of the nation’s gross domestic product, a share that most economists say is plenty acceptable.

But Obama has undeniably planted a stake in the middle ground in the current fiscal policy debate, between the $1 trillion in taxes but no entitlement curbs budget of the Senate Democrats and the $4.6 trillion in cuts but no new revenues approach of the House Republicans’ blueprint.

The president has made clear he’s prepared to stand pat in that spot until the GOP moves toward him on taxes, that he’ll never move farther away from his congressional Democratic base. He’s betting that he’ll be a winner either way from that posture: His fiscal policy legacy will be secure if Republicans start talking taxes and a big deal gets done, or his party’s midterm fortunes will be enhanced if there’s a standoff on which he can blame GOP intransigence.

The outcome will be known by the end of July.