Pablo Martinez Monsivais/AP

Continuing his congressional outreach campaign, President Obama has invited House Budget Committee Chairman Paul Ryan, R-Wis., and the top Democrat on the committee, Rep. Chris Van Hollen of Maryland, to lunch at the White House today.

Their meeting is the latest in a series of discussions the president is having with rank-and-file Republicans and Democrats as he tries to jump-start budget negotiations.

Ryan, the former Republican vice presidential nominee respected within the GOP conference as its leading expert on the budget, is pivotal to any bipartisan budget deal. He is expected to introduce a new budget next Tuesday.

Today's luncheon comes after the president and 12 Republicans senators, including four members of the Senate Budget Committee, met for a rare dinner Wednesday night at the Jefferson Hotel in downtown Washington. After dining together for more than two hours - the president picked up the tab - the senators expressed optimism at the prospect of reaching a deal to reduce the deficit.

"The president greatly enjoyed the dinner and had a good exchange of ideas with the senators," said a senior administration official.

The president's charm offensive, the most intense direct discussions he has had with Republicans in years, comes after the White House and Republicans failed to reach an agreement last week to avert across-the-board sequester spending cuts. The president continues to insist that any package to replace the cuts must be a balance between spending cuts and new tax revenue. Republicans, however, continue to oppose any tax increases as part of a package to replace the sequester.

The courtship will continue next week when the president meets separately with both parties in both the House and Senate on Capitol Hill. The president will face his harshest critics, the House Republicans, in a members-only meeting in the Capitol basement next Wednesday afternoon.

"We want to welcome the president to come up and talk to our members, and I'm looking forward to it," House Speaker John Boehner said today at a Capitol news conference.

Boehner expressed shock at the president's latest outreach, calling it an "180 degree" turn from his approach in the past, but the speaker warned the president not to continue asking for new tax revenue as part of a deal to reduce the deficit.

"After being in office now for four years, he's actually going to sit down and talk to members," Boehner said in sarcastic disbelief. "I'm hopeful that something'll come out of it, but if the president continues to insist on tax hikes, I don't think we're going to get very far."

Asked whether she believes the president's overtures will produce results, House Minority Leader Nancy Pelosi said the discussions are "important" for the president "to understand the motivation of members and what the possibilities are in terms of courage."

"It's important that they all get to know each other better," Pelosi said.

But Pelosi seemed weary of the discussions and recalled how she told the president to stop wasting his time entertaining direct talks with Republicans.

"This president has been so respectful, given so much time to the Republicans and their views, to the point that at one time in one of our meetings I said to the president, 'Mr. President, I'm busy and I don't have any more time for this. You have to be the busiest person in the world. If and when they come up with a new idea, why don't we just call you back into the room.'"

Boehner said many members have "good ideas" around Congress, and he believes that the more members that leadership and the White House engage in negotiations "the better off we are."

"If you're ever going to pass a major bill that will begin to address our spending problem, we're going to grow this support, and it's going to have to be an organic process," he continued. "It's a hopeful sign, and maybe something'll come of it."