Nothing, it seems, can bridge the bottomless political divide in Washington over taxes and spending.

Not an election last November that gave President Barack Obama a second term. Not polling that shows a strong majority of Americans want both sides to compromise in forging an agreement to reduce chronic federal deficits and debts.

Not the president's new personal outreach to Congress, including a 90-minute meeting Wednesday with House Republicans. And not even white smoke from the Vatican chimney that signaled selection of a new pope as the talks occurred.

"You are straining the analogy," Obama told reporters afterward when asked if the meeting produced any similar message of spiritual significance.

Leaders on both sides acknowledged the deep differences between them on a day when congressional committees began considering separate spending proposals for 2014 to launch the formal budget process.

In an interview broadcast Wednesday on ABC, Obama warned that compromise may prove unattainable.

"Right now what I'm trying to do is create an atmosphere where Democrats and Republicans can go ahead and get together and try to get something done," he said of his so-called charm offensive that has included a dinner with GOP senators, lunch with House leaders and meetings with others legislators. "But ultimately it may be that the differences are just too wide."

House Speaker John Boehner labeled Obama's visit to the Capitol on Wednesday "productive" because it allowed both sides to understand the "very real differences" between the parties.

"Republicans want to balance the budget. The president doesn't," Boehner said. "Republicans want to solve our long-term debt problem. The president doesn't. We want to unlock our energy resources to put more Americans back to work. The president doesn't."

He then came to either his punch line or understated conclusion: "But having said that, today was a good start, and I hope that these kinds of discussions can continue."

Earlier, House Budget Committee Chairman Paul Ryan also recognized the challenge, telling the panel's first meeting on his proposed budget for next year that Congress faced a tough negotiation.

"We are hoping that at the end of the day, we're still talking to each other and we can make a down payment" on balancing the federal budget, said Ryan, R-Wisconsin.

On the Senate side, Budget Committee Chairwoman Patty Murray made her own joking reference to the papal decision as the panel began considering the first full Democratic spending plan in recent years.

"I understand we have a new pope and a committee hearing to mark up a budget. That's history twice, so it's good," said Murray, D-Washington.

Turning serious, she added that "this process is not going to be easy" because of "a serious difference of opinion about what our government should be doing to keep our economy and our national finances moving in the right direction."

The proposal by Senate Democrats called for a mix of increased tax revenue and spending cuts to reduce deficits by about $1.9 trillion over 10 years.

It would increase revenue by about $975 billion by eliminating and curtailing tax breaks and loopholes for wealthy Americans and corporations. It would also cut spending by an estimated $975 billion: $493 billion in domestic spending; $240 billion in defense spending; and $242 billion in interest savings.

The proposal included a $100 billion economic stimulus package for road and bridge repairs, as well as worker training, that Murray said would be paid for by curtailing tax breaks for high-income households and corporations.

However, the Senate plan avoided significant changes to popular entitlement programs such as Medicare and Medicaid, which are major drivers of federal deficits.

Republican leaders oppose new tax hikes or revenue and demand substantial overhauls of entitlement programs, setting up another in the litany of congressional impasses of recent years.

At the White House, spokesman Jay Carney told reporters that Obama's new outreach was intended to find "common ground" on a deficit reduction plan that would include reforms of the tax system and popular entitlement programs.

Obama will introduce his own budget proposal next month, and the president and Democrats concede their approaches would not eliminate annual deficits, as sought by Republicans, but instead reduce them to what they say are manageable levels.

Republicans call such an approach inadequate, insisting that government has become too large and costly to ensure needed economic growth.

Ryan proposed a conservative budget for fiscal year 2014, which begins on October 1. He said it would eliminate the annual deficit in a decade without raising taxes.

It 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.