President Barack Obama wrapped up three days of personal outreach on Capitol Hill, holding what both sides called a "great" meeting on Thursday with Senate Republicans who urged him to deliver the necessary Democratic support for making needed reforms to popular entitlement programs.

"He certainly understands that you can't fix the country without adjusting entitlements to fit the demographics of our country," said Senate GOP leader Mitch McConnell, usually a harsh critic of the president. "And we'll see where we go from here, but it was a great meeting."

For his part, Obama labeled the more than 90-minute meeting as a "great conversation" as he headed to a separate gathering with House Democrats opposed to significant changes to Medicare and Medicaid, which provide health care to senior citizens, the poor and the disabled.

After the second meeting, Obama said progress was made, and some House Democrats expressed willingness to discuss changes to entitlement programs as part of a broad agreement that would include GOP concessions on taxes.

The two meetings concluded a week of what reporters dubbed Obama's "charm offensive" -- a series of talks with legislators -- as Congress began debating budget proposals for 2014.

A formal budget process, with both chambers considering separate plans from each party that would be debated and negotiated in coming months, is considered the last opportunity this year to forge a compromise on reducing the nation's chronic federal deficits and debt.

Such an agreement proved unreachable in Obama's first term and the president emphasized during his meeting with Senate Republicans on Thursday that he sought bipartisan solutions to major issues after his re-election, according to participants.

"He mentioned there are some theories out there that he's trying to lure everyone into a trap, if you will, as a way to take back the House or whatever, and he assured us he's simply trying to get a budget deal done," said Sen. Jeff Flake, R-Arizona. "So as much as our base or others are convinced the president has nefarious motives, he challenged us to challenge them on that."

In addition, Obama told the GOP senators that "he's going to have to bring some people from his party along on entitlement reforms who don't want anything to happen, and he challenged us to do the same," Flake said.

Asked if any of the meeting could be labeled contentious, Flake answered "no."

The positive response, with none of the usual partisan rhetoric that has dominated political debate in Washington, signaled that both sides perceived a willingness in the other to tackle at least some of the tax and spending issues that have proven intractable in recent years.

"We need from him two things," said McConnell, R-Kentucky. "He needs to be directly involved, not -- as we used to say -- leading from behind, but directly involved. And his job is to deliver the members of his party."

In particular, he said, Obama must explain the need for entitlement reforms.

Obama's liberal base opposes any significant changes to entitlements, arguing senior citizens paid into the programs during their lives and deserve the benefits promised them such as health care coverage and Social Security checks.

"Only one person in the government has a big enough pulpit to explain that," McConnell said.

In the meeting with House Democrats, Obama discussed entitlement reforms including his offer to tighten the adjustment for inflation of benefits such as Social Security, meaning annual increases for future recipients would grow at a slower pace, according to participants.

Opponents of the reform, known as "chained CPI" in reference to the Consumer Price Index it involves, argue it hurts senior citizens and others who most need their benefits.

However, some House Democrats indicated after the meeting they were open to discussing such a change if Republicans showed they were open to increased tax revenue.

"We're not going to entertain any significant entitlement conversation until the Republicans meet us halfway with a revenue conversation," said Rep. G.K. Butterfield, D-North Carolina. "Those two conversations must be able to happen at the same time."

Rep. Nita Lowey, D-New York, said she opposed the chained CPI idea, but was willing to discuss it because Obama told the meeting there could be exceptions to protect "the most vulnerable."

Meanwhle, McConnell and other GOP senators said they agreed with Obama in their meeting on the need to overhaul the corporate tax system to lower rates in order to make American companies more competitive abroad.

However, House Speaker John Boehner offered a less optimistic view a day after Obama met with House Republicans, telling reporters that "this is going to take more than dinner dates and phone calls."

"The president's idea of compromise is just 'do it my way,' and that's not going to work," Boehner said in reference to the call by Obama and Democrats for increased tax revenue to be part of any compromise on deficit reduction.

Noting that Congress approved a return to higher tax rates of the 1990s on top income earners in January, Boehner said Obama "got his tax hikes" in that deal and "now it's time to cut spending."

White House spokesman Jay Carney said Obama was fully aware of the "enormous obstacles" to compromise.