As House Budget Chairman Paul Ryan released his balanced budget blueprint today, the former Republican vice presidential nominee issued a direct challenge to President Obama to present his own plan to balance the federal government's books.

"This is an invitation. Show us how to balance the budget," Ryan, R-Wis., said at a Capitol news conference today. "If you don't like the way we're proposing to balance our budget, how do you propose to balance the budget?"

With a plan that balances spending and revenue over the next decade without increasing taxes, Ryan is back in the spotlight after keeping a low profile following last year's failed campaign with Mitt Romney.

Ryan, who has proven to be one of President Obama's fiercest economic critics in Washington, said Republicans "owe the country a balanced budget."

"The election didn't go our way. Believe me, I know what that feels like. That means we surrender our principles? That means we stop believing in what we believe in?" Ryan said. "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're showing our answers."

Ryan's budget, known as "The Path to Prosperity: A Responsible, Balanced Budget," would cut $4.6 trillion in spending by 2023, decreasing the net spending from $46 trillion to only $41 trillion over the next decade. It also proposes to repeal the president's health care law, simplify the tax code into two brackets, as well as cut Medicare and federal pensions.

"We cut wasteful spending," Ryan said. "We repair the safety net so that we can help those in need. We protect and strengthen key priorities like Medicare, a program that's going bankrupt, that's jeopardizing the health security for millions of American seniors, and we foster a healthier economy so that we can create jobs and grow more wages."

Beyond savings from sequestration and $600 billion in new tax revenue from the Fiscal Cliff deal, Ryan said that reforming pension programs for the federal workforce and extending the Budget Control Act's discretionary caps for two more years "makes it easier for us to balance the budget" than his previous budget proposals.

"We don't think that federal employees should be able to have pension systems that are so far in excess of what their private sector counterparts get," Ryan said. "[A balanced budget] helps give us a healthy economy and a pro-growth economy. It helps make sure that our kids inherit a debt-free nation. This is a goal that all of us should have, whether we're Republican or Democrat."

"This is our offer," Ryan said. "This is our vision, and what you do is you actually show the country what you believe in."

White House Press Secretary Jay Carney issued a statement, contending "the math just doesn't add up" in the House Republican budget proposal.

Carney said the president's budget proposal will put the country "on a fiscally sustainable path."

"While the president disagrees with the House Republican approach, we all agree we need to leave a better future for our children," Carney stated. "The president will continue to work with Republicans and Democrats in Congress to grow the economy and cut the deficit in a balanced way."

President Obama is at the Capitol this week meeting with each party's caucus in the House and Senate. The president meets with the House Republican Conference on Wednesday afternoon.

House Minority Leader Nancy Pelosi said the Ryan budget is "nothing more than more of the same" and predicted it would have an adverse economic impact if enacted into law.

"Americans deserve better than the same old fuzzy Republican math and budget gimmicks," Pelosi, D-Calif., said in a statement. "It still destroys jobs and puts our economic recovery at risk. It still protects the wealthiest at the expense of the middle class. It still undermines the health and economic security of the elderly and disabled. It still ends the Medicare guarantee and shifts costs to seniors."

Rep. Chris Van Hollen, the Democrats' ranking member on the Budget Committee, is expected to submit an alternative Democratic budget later today.

ABC News' Mary Bruce contributed to this report