The GOP plan came as President Barack Obama traveled to Capitol Hill to meet with Senate Democrats on the budget and a broad range of other proposals that are part of his second-term agenda. The president has launched a new outreach to rank-and-file Republicans, and his Hill visit is one of several planned with lawmakers of both parties this week.

The fiscal blueprint released Tuesday by Budget Committee Chairman Paul Ryan, R-Wis., will be dead on arrival with the White House and Democrats controlling the Senate. But the point is to prove it’s possible to balance the budget within 10 years by simply cutting spending and avoiding further tax hikes.

The latest Ryan plan generally resembles prior ones, relying on higher tax revenues enacted in January and improved Medicare cost estimates — along with somewhat sharper spending cuts — to promise balance.

Senate Democrats plan to offer a counterproposal on Wednesday with higher spending on domestic programs and additional tax hikes on top of the higher rates imposed on top-bracket earners in January. That plan will, in turn, arrive as a dead letter in the GOP-controlled House.

Aides familiar with the Senate Democratic plan said it would curb deficits by $1.85 trillion over the coming decade, with $975 billion coming from new revenues and $975 billion coming from new spending cuts. The aides required anonymity because the budget is not public but said the plan would generate $275 billion in health care savings not made through cutting benefits.

At issue on Tuesday and beyond is the arcane and partisan congressional budget process, one that is unlikely to illustrate a path forward in a gridlocked Washington. At stake are so-called budget resolutions, which are nonbinding measures that have the potential to stake out parameters for follow-up legislation cutting spending and rewriting the complex U.S. tax code.

But this year’s dueling GOP and Democratic budget proposals are more about defining political differences — as if last year’s elections didn’t do enough of that — than charting a path forward toward a solution. Congressional budgets often simply state party positions, and invariably are partisan endeavors.

Ryan, who became a national GOP figure as the losing vice presidential nominee last year, has for now settled back into his wonkish role as Budget Committee chairman and chief tutor for dozens of relatively junior Republicans. He’s also armed with a full battery of budget bromides.

“You cannot continue to kick the can down the road,” Ryan said Tuesday. “You cannot continue to spend money we just don’t have.”

“On the current path, we’ll spend $46 trillion over the next 10 years. Under our proposal, we’ll spend $41 trillion,” Ryan said in an op-ed in the Wall St. Journal. “On the current path, spending will increase by 5 percent each year. Under our proposal, it will increase by 3.4 percent.”

Ryan’s plan promises to cut the deficit from $845 billion this year to $528 billion in the 2014 budget year that starts in October. It would drop to $125 billion in 2015 and hover pretty much near balance for several years before registering a $7 billion surplus in 2023.

The White House weighed in against the Ryan plan, saying it would turn Medicare into a voucher program and protect the wealthy from tax increases.

“While the House Republican budget aims to reduce the deficit, the math just doesn’t add up,” said White House Press Secretary Jay Carney. “Deficit reduction that asks nothing from the wealthiest Americans has serious consequences for the middle class.”

The House Budget Committee has scheduled a vote on the measure Wednesday, and the Senate Budget panel is slated to vote Thursday on rival legislation by new Budget Committee Chairwoman Patty Murray, D-Wash., who promises new tax revenues but few cuts from domestic programs like Medicare and Medicaid.

Murray outlined her own budget plan at a closed-door meeting of the rank and file during the day. According to officials familiar with the details, it calls for $1.95 trillion in deficit savings over a decade, $975 billion from unspecified higher taxes, $735 billion in reduced spending and $240 billion in lower interest costs.

It also recommends $100 billion in new spending for job training, water and sewer construction and other public works projects.

Medicare would be in line for $265 billion in savings over a decade, and another $10 billion would come from Medicaid. Farm programs would take a cut of $23 billion over a decade.

As part of the overall savings, the budget would also eliminate the across-the-board spending cuts that recently took effect, and replace them with a blend of tax increases and spending cuts.

“We are working towards fair and balanced, which is what the American public has said time and time again that they want,” Murray said. “We need to make sure that everybody participates in getting us to a budget that deals with our debt and our deficit responsibly.”

For his part, Ryan has resurrected a controversial Medicare proposal that replaces traditional Medicare for those currently under 55 with a government subsidy to buy health insurance on the open market. Critics of the plan say the subsidies won’t grow with inflation fast enough and would shove thousands of dollars in higher premiums onto seniors before very long.

The House GOP plan again proposes sharp cuts to the Medicaid health program for the poor, tighter food stamp eligibility rules and claims $1.8 trillion in savings over a decade by repealing Obama’s signature overhaul of the U.S. health care system. It generally seeks to preserve the Pentagon budget, but only at the expense of proposing dramatic cuts to domestic agency budgets that may prove too low for GOP moderates and the pragmatists atop the Appropriations Committee responsible for guiding them into law.

A document released Tuesday offers few specifics on the proposed cuts to domestic programs, but it generally appears to incorporate spending levels for day-to-day agency operations significantly below levels called for by controversial automatic spending cuts. They are just starting to take effect though their bite has yet to cause broad-based pain.

Even as it proposes repealing Obamacare, the Ryan plan preserves more than $700 billion in the health care law’s cuts to Medicare providers over a decade — just as more than $600 billion in tax hikes on the wealthy enacted in January make it easier for Ryan’s budget to predict balance.

Ryan also proposes overhauling the tax code by eliminating many or most tax deductions and using the savings to lower income tax rates, with a top rate of 25 percent instead of 39.6 percent.