President Obama’s $3.78 trillion budget Wednesday provided fresh, vivid evidence that Washington remains desperately divided over key spending and tax issues — and that government appears poised to keep limping along without a broad budget agreement.

Unable to reach agreement to cut spending or raise taxes, that means the federal government is likely to be funded by yet another “continuing resolution,” or stopgap spending bill, extending the status quo of current spending and tax policies when the next fiscal year starts on Oct. 1.

About all that will be clear in the coming weeks is that Washington is once again deadlocked. Three different visions of how government should work are now on the table, as Senate Democrats and House Republicans approved their own very different versions last month.

Obama tried to offer some compromise Wednesday, most notably by proposing to slow the annual increases in Social Security benefits. But he convinced no one on Capitol Hill that a grand bargain is within reach to stop the nation’s $17.2 trillion debt from continuing to grow, let alone start to shrink.

“I don’t think we should talk about a grand bargain,” House Budget Committee Chairman Paul Ryan, R-Wis., said flatly.

The gaps are too wide. Obama and Democrats want higher taxes, Republicans refuse.

Obama and Republicans disagree sharply on the future of Medicare. Republicans want to allow seniors the choice of private coverage or Medicare starting in 2024. Democrats are opposed.

Obama proposed slowing the growth of Social Security benefits in his new budget. Democrats were not pleased.

Most critically, Republicans want the budget to eventually return to balance. Democrats see that as unrealistic anytime soon. Both Obama and Senate Democrats peg their lowest annual deficits over the next decade at around $400 billion.

All these are profound disagreements, unlikely to be resolved in a matter of months, perhaps even years. Some progress has been made, notably the 2011 deal to reduce anticipated deficits with less spending, and the New Year’s Day measure to raise an additional $600 billion.

Obama on Wednesday touted his new plan as an effort to inch toward the Republicans. Republicans weren’t buying it. “It doesn’t break new ground,” Ryan said. Added House Speaker John Boehner, R-Ohio: “We don’t need to be raising taxes on the American people.”

Democrats were lukewarm, largely because of the proposed change in the way Social Security benefits are increased to reflect higher cost of living. Rep. Chris Van Hollen of Maryland, the top Democrat on the House Budget Committee, said he had “concerns with aspects of this budget.”

Few spoke on Capitol Hill about breakthroughs.

“Every time I read something about John Boehner it sounds totally unreasonable,” said Sen. Tom Harkin, D-Iowa, who heads the Senate subcommittee that writes legislation on health, education and labor-related spending. Boehner insists that Obama got $600 billion in new revenue in the January fiscal cliff agreement, so this is no time to seek more.

“How can you deal with someone who takes that kind of position?” Harkin asked.

Republicans also were not optimistic. “It’s a wide chasm,” said Sen. Jeff Flake, R-Ariz., a longtime activist on budget issues.

The gap is widest on the four issues that have dominated the budget debate for years: Medicare and other entitlements, taxes, domestic spending and the deficit. The outlook:

Medicare and entitlements. Obama is willing to take steps that would cut about $401 billion in anticipated federal health spending over 10 years. Wealthy beneficiaries would pay higher Medicare premiums, and lower-income people would get incentives to use generic drugs.

There probably could be some bipartisan agreement on using, beginning in 2015, the “chained Consumer Price Index” method of calculating cost-of-living increases for Social Security and other government programs.

Complaints take two forms. Republicans say Obama’s not going far enough, and Democrats complain he’s hurting those who can least afford the pain. Obama, said Sen. Bernard Sanders, a Vermont independent, is “walking down a very perilous path” with such proposals.

Taxes. Both Obama and Senate Democrats want to raise nearly $1 trillion in new revenue over the next 10 years. Obama’s plans include higher taxes for the wealthy and nearly doubling the tobacco tax to help pay for a new preschool program. Republicans offer no new taxes.

Domestic spending. The first round of automatic spending cuts, totaling $85 billion, went into effect March 1, and more such reductions are coming.

Obama and Senate Democrats have similar spending aims. Both would end the automatic spending cuts, or sequester. Democrats replace the sequester with more targeted reductions as well as increases in spending on infrastructure and other programs.

Senate Democrats propose $493 billion in unspecified domestic reductions over 10 years, including $275 billion saved from health care programs “in a way that does not harm seniors or families.” Obama’s health care savings are similar.

Republicans would retain most of the automatic cuts. Some money would be added back to the Pentagon budget, taken from domestic agencies. They would also repeal the 2010 law overhauling the nation’s health care system.

Deficit. The federal deficit is estimated to total $973 billion this year.

Republicans insist it’s important to bring the budget back to surplus, and would do so by 2023. Democrats see that as an unrealistic goal. The Senate Democrats’ plan would reduce annual deficits to around $400 billion in about three years, while Obama’s plan would lower the deficit to $439 billion by 2023.

Those numbers made Republicans howl. Obama on Wednesday tried to deflect the barbs and sell the package as a pastiche of tough choices.

Instead, he created bipartisan agreement on one point — reaching a broad accord will be tough, if not impossible.

“Minor reforms,” said Sen. Bob Corker, R-Tenn., considered open to bipartisan dialogue. Added Senate Appropriations Committee Chairwoman Barbara Mikulski, D-Md., usually an Obama loyalist, “There are specifics in the president’s plan around earned benefits about which I have serious concerns.”