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The competing budgets, both unlikely to get through Washington's divided government in their current form, raised fresh doubts about Congress reaching a compromise on taxes and spending, which polls consistently show the public wants more than any specific plan.
Instead, they appeared crafted to appeal to their respective party bases.
The Republican proposal, sponsored by House Budget Committee Chairman and former Republican Vice Presidential candidate Paul Ryan, promises to balance the budget without raising taxes in ten years. It would eliminate President Obama's health care overhaul and make large cuts in spending, particularly to so-called safety-net programs such as Medicare and Medicaid, the government health insurance plans for seniors and the poor.
Ryan is a likely contender for the 2016 Republican presidential nomination, and the proposal could serve him well in primary races where conservatives wield the most influence.
The Senate Democratic budget proposal, which began leaking out just as Ryan announced his proposal, would shrink budget deficits by $1.85 trillion over 10 years but not balance the budget. It is largely the work of Democratic Senator Patty Murray of Washington, who heads the Senate Budget Committee.
It would rely on an equal mix of spending cuts and tax hikes on the wealthy. At the same time, it would create a $100 billion fund for rebuilding crumbling roads and bridges, creating construction jobs.
Both parties claim backing from voters; Republicans because they were returned to power in the House in 2012; Democrats because Obama was re-elected.
Over the past week the Democratic president has begun wooing Republicans in Congress to work with him on a "grand bargain" to corral budget deficits that have topped $1 trillion in each of the past four years.
Republican lawmakers who dined with Obama in recent days said they were encouraged by their meetings.
But with proposals actually being put down on paper, in the form of 2014 budget blueprints, the air of bipartisanship seemed to evaporate, at least for now - even as Obama huddled Tuesday just off the Senate chamber with fellow Democrats to urge progress.
Indeed, among the warnings Obama got from some Democrats, according to Senators who attended the meeting, was not to cut safety-net programs.
"These were two ideological documents. They are both bargaining positions," said David Brown, a policy analyst at Third Way, a centrist think tank in Washington.
Brown added that for a budget compromise to be reached in coming months, Obama will have to convince the public of the need to reform "entitlement" programs, such as Medicare and Medicaid, although not necessarily as drastically as the Ryan budget requires.
Ryan, a leading conservative voice in Congress, took the wraps off of his budget outline for fiscal 2014 that begins October 1 and chastised the Obama administration for overseeing a rapid run-up in debt that now totals $16.7 trillion.
"You can't start really paying this debt down in a serious way until you balance the budget," he said. "The current high levels of debt we have today are a threat to our economy."
Ryan's budget, with its $4.6 trillion in deficit reduction over 10 years, was welcomed by Republicans in Congress. It was similar to the budget Ryan proposed for fiscal 2013 that won approval in the Republican House.
But its deep cuts in social safety net programs coupled with significant tax cuts for upper-income Americans, was roundly criticized by Democrats.
Democratic Senate Majority Leader Harry Reid of Nevada even challenged the Ryan plan's claim of achieving balance by 2023, saying it "relies on accounting that's creative at best and fraudulent at worst."
A senior Republican senator, Jerry Moran of Kansas, dismissed Murray's 2014 budget blueprint, saying, "all the Democrats can come up with for a budget is a trillion-dollar increase in taxes."
A gulf to bridge
As has been the case since early 2011, when deficit reduction took center stage, Democrats and Republicans were fighting over the same, fundamental questions: Should budget deficits be attacked with spending cuts, tax increases or a combination?
A McClatchy-Marist poll released Tuesday showed that Democrat respondents prefer increasing taxes over cutting spending by a margin of 65% to 27%.
The pattern was reversed for Republicans surveyed, who preferred cuts to tax increases by 79% to 14%. Support for cuts declined when specific programs are mentioned.
But seven in ten of all those polled said they believed it is more important "for government officials to compromise" to find a solution than to insist on their own goals.
"The gulf we have to bridge is just as big as it ever was," said Representative Chris Van Hollen of Maryland, the top Democrat on the House of Representatives Budget Committee.
But for all the squabbling washing over Capitol Hill on Tuesday, Obama did not seem rattled.
Senator Benjamin Cardin, a liberal Democrat from Maryland who attended Tuesday's lunch with Obama, told reporters: "On the budget issues, he acknowledged that 'look, the best course now, is to let the budgets go, get them into conference, and try to reconcile the two.'"
In other words, the president advised each side to pass their respective budgets, ones that will appeal to their core political supporters, and then work out the differences the old-fashioned way in a House-Senate negotiating group.
That will be a complicated task however and Obama got a taste of it from liberal Democratic senators who at lunch expressed their concern with the president's willingness to potentially cut social programs like Social Security retirement benefits and Medicare healthcare for the elderly and disabled.
As Obama reaches across the aisle, his approval rating jumped up four percentage points from last week to 47%, according to a Reuters/Ipsos online poll released on Tuesday. But the percentage of Americans who disapprove of his performance at 50% was still higher than his approval rating. Fifty-seven percent of people said the country is going in the wrong direction, compared to 27% who think it is on the right track.
Meanwhile, a budget brush fire erupted on another front on Tuesday.
Legislation in the Senate to avert a March 27 government shutdown was being slowed by Republican senators. They expressed concerns over how money was being spent in the Democratic bill to fund federal agencies through September 30.
Leaders in the Senate and House of Representatives are nonetheless hoping to finish this short-term funding bill by next week.
