Despite a ballyhooed charm offensive by President Barack Obama, political leaders continued talking past each other on Tuesday in proposing partisan ideas on taxes and spending that have zero chance of winning congressional approval.

Obama met with Senate Democrats in the first of three visits to Capitol Hill this week for face time with legislators from both parties.

The rare personal appearances by the president, a former senator, follow his newly unveiled outreach efforts that included dinner with Senate Republicans and lunch with two influential House members last week, as well as phone calls to various legislators from both parties.

Obama offered no comment to reporters when entering and departing Tuesday's meeting with senators, while White House spokesman Jay Carney rejected any inference that the meetings and phone calls by the president were just for show.

Democratic senators who met with Obama described him as upbeat and supportive.

Sen. Carl Levin of Michigan said Obama called compromise with Republicans essential, but added that the president acknowledged "he hasn't seen enough from them yet."

Another participant, Sen. Ben Cardin of Maryland, said Obama stayed longer than expected to answer "about a dozen questions" on fiscal issues and other topics, noting that he "obviously wanted to be there."

The top Senate Republican, Mitch McConnell of Kentucky, said he welcomed Obama's efforts, adding: "I think having more of that rather than less of that is a good idea."

Democratic senators who met with Obama on Tuesday described the president as upbeat and supportive.

Whether symbolic or sincere, Obama's increased personal engagement came as Congress prepared for the first formal budget debate since the president took office four years ago.

However, all signs Tuesday indicated the issues and rhetoric would be much the same as during the repeated political showdowns that marked the president's first term.

House Budget Committee Chairman Paul Ryan fired the opening salvo, introducing a conservative budget proposal for fiscal year 2014 that he said would eliminate the annual deficit in a decade without raising taxes.

"We think we owe the country a balanced budget," Ryan told reporters. "We think we owe the country solutions to the big problems that are plaguing our nation -- a debt crisis on the horizon, a slow growing economy, people trapped in poverty. We are showing our answers."

The Wisconsin Republican's plan calls for cutting $5 trillion from projected spending increases in the next 10 years while lowering tax rates and getting rid of most of Obama's signature legislation of his first term -- the 2010 health care reform law.

Ryan also revived his controversial proposal to reform Medicare, the health care program for senior citizens that is considered the biggest driver of rising federal deficits as costs increase and more Americans become eligible.

The idea was a major issue in last year's presidential election, in which Ryan was the vice presidential candidate on the GOP ticket that lost to Obama.

It calls for offering senior citizens a choice between traditional fee-for-service Medicare and a premium support system that would provide a fixed government payment to help them buy private health insurance. The plan would take effect in 2024 to exempt people 55 and older today.

Democratic rejection of much of Ryan's approach was swift with the White House saying that his math didn't add up, using language from policy debates of last year's election campaign.

"If instead of asking the wealthiest to contribute to deficit reduction, you say we'd like to give the wealthiest a huge tax cut, the result is that ... the burden is doubled or tripled on everyone else and that just doesn't seem fair and it's also not good economics," presidential spokesman Jay Carney told reporters.

Obama followed up.

"We're not going to balance the budget in 10 years," he said in an interview with ABC News. "If you look at what Paul Ryan does to balance the budget, it means that you have to 'voucherize' Medicare, you have to slash deeply into programs like Medicaid, you've essentially got to either tax middle class families a lot higher than you currently are or you can't lower rates the way he's promised."

Senate Majority Leader Harry Reid, D-Nevada, contended that Ryan's proposal was "even more extreme" than Republican policies rejected by voters in the November election.

For his part, Ryan noted that "the election didn't go our way," but asked whether that meant Republicans must surrender their principles.

However, he sounded contradictory when challenged about his call to eliminate most of Obama's health care reform law. After first saying "we are not going to re-fight the past" and that "law is law" with regard to the measure known as Obamacare, Ryan later said that "we need to repeal and replace Obamacare with a better system."

Senate Democrats plan to make public their own 2014 budget proposal on Wednesday, and Reid confirmed it would call for an equal amount of increased tax revenue from wealthy Americans and spending cuts to help bring down deficits.