All true. But from Biden’s standpoint, the budget rollout was a resounding success that served two purposes.

It put the president where he wants to be as he prepares an expected reelection campaign, with one foot in his party’s center and one in its progressive left.

Biden gave centrists a promise to cut future deficits by almost $3 trillion and shore up Medicare’s deteriorating finances.

But he also asked for more funding for child care, elder care and fighting climate change, and said he’d pay for the whole package by raising taxes on corporations and the wealthy.

In a campaign-style speech at a union hall in the swing state of Pennsylvania, he said his budget was designed to “give working-class folks a fighting chance.” Expect to hear more of that as he tries to woo those voters next year.

More important, the budget was Biden’s opening offer in a battle over federal spending that is likely to consume the rest of the year.

The president knows the Republican-led House of Representatives won’t agree to the social programs he’s proposed or the tax increases to pay for them.

Beyond campaign positioning, his real goal was to nudge House Republicans toward serious negotiations and a vote to raise the debt ceiling, which limits government borrowing.

Republicans have said they won’t raise it unless they get deep spending cuts in return — an ultimatum that risks touching off a catastrophic failure by the government to pay its bills. But they haven’t settled on a comprehensive list of the cuts they want; there’s no official GOP budget proposal.

They’ve mostly recycled traditional conservative demands for cuts in spending they consider wasteful, plus one innovative wrinkle: They’ve promised to trim the budget by eliminating “woke spending.”

And what, you may ask, is that? The definition isn’t clear.

Judging from the examples Republicans offer, woke spending appears to include anything conservative voters don’t like: racial equity efforts, especially in the armed forces; programs aimed at helping LGBTQ people; and anything to do with climate change.

Plus a walking trail in the Atlanta suburbs. A $3.6-million federal grant to extend the Michelle Obama Trail is on the House Budget Committee’s hit list of “woke waste.” If the DeKalb County Board of Commissioners had named the path after Rosalynn Carter, it might not be in as much trouble.

But cutting every penny of so-called woke spending, no matter how broadly the term is defined, won’t eliminate the deficit.

The “woke waste” list was compiled by House Budget Committee Chairman Jodey Arrington (R-Texas), who has offered the closest thing Republicans have to a plan.

Arrington has proposed cutting domestic spending by $150 billion next year. That sounds like a lot, but it would reduce the federal deficit by only about 9%.

And that gets us to the House Republicans’ real problem: They’ve boxed themselves in to a fiscal trap, thanks mostly to former President Trump.

For decades, conservatives proposed balancing the budget partly by cutting future spending on Social Security and Medicare.

But Trump abandoned that doctrine, and other Republicans, including House Speaker Kevin McCarthy of Bakersfield, fell in line — even though fiscal experts in both parties acknowledge that the programs are heading toward financial trouble.

So while Republicans want spending cuts, they have ruled out taking them from the biggest programs: Social Security, Medicare and defense.

To balance the budget within 10 years, as they say they want to do, they would need to cut almost every other part of the government by an unrealistic 85%, according to the nonpartisan Committee for a Responsible Federal Budget.

Biden has taken Social Security and Medicare off the table, too, but he has built himself an escape hatch: He wants to raise taxes on corporations and people who make more than $400,000 a year. That would allow him to put money into Medicare and reduce the national debt.

Republicans have sworn never to raise taxes, so they need to find another solution to the math problem. They haven’t.

That’s why the danger of a budget crisis — not only a government shutdown, but a catastrophic default on the federal debt — looks greater this year than ever before.

The way to avert such a crisis is to begin serious negotiations. Biden’s budget proposal has put the ball in McCarthy’s court. Where’s his plan?