On the one hand, many Republicans who long have chided Obama for failing to engage their party on the nation's biggest problems are applauding his newfound outreach - part of a concerted effort by the president to mend ties with Congress in hopes of reaching a grand compromise on fiscal issues.
On the other hand, neither side is backing down from entrenched positions that have prevented deals in the past.
Exhibit A: the House GOP's new budget proposal, crafted by House Budget Committee Chairman Paul Ryan, R-Wis., who ran against Obama as the 2012 Republican vice presidential nominee but broke bread with him last week as the president initiated his congressional "charm offensive."
Ryan and House Republicans, who were to meet with Obama at the Capitol on Wednesday, put forward their 2014 budget fully mindful that it would be dead on arrival at the White House and in the Democratic-controlled Senate. The plan, which the White House immediately panned, doubles down on longstanding Republican proposals to slash funding for programs Obama and Democrats sorely want to protect. It includes a repeal of Obama's health care law - a major component of his legacy - and Medicare changes that would shift more of the cost to future patients.
At the same time, Obama hasn't budged from his insistence that any budget include new tax revenues - the key sticking point in February's failed attempt to avert $85 billion in automatic spending cuts that both parties agreed made for bad policy. And Senate Democrats were to unveil a counterproposal Wednesday that aides said would raise taxes by almost $1 trillion and would use savings to repeal the automatic spending cuts - a nonstarter for House Republicans.
The resolve from both sides to dig in their heels on the most contentious issues raises an important question about Obama's efforts to make nice with Republicans: What's the point?
"We're not naive. There are disagreements and obstacles," White House press secretary Jay Carney said. "But the president is at the head of this effort because he believes deeply in it."
In reaching out to lawmakers, Obama hopes to attract more moderate elements from both parties in Congress to deal comprehensively with the nation's long-term fiscal imbalance. The fence-mending campaign started with a dinner Obama hosted last week at a hotel near the White House for a dozen Senate Republicans and continues this week with the House GOP meeting Wednesday and a pair of closed-door sessions with House Democrats and Senate Republicans on Thursday.
In interviews and on Sunday talk shows, many Republicans on the receiving end of Obama's overtures have praised the president for making an effort - even if they feel it's too little, too late.
"We welcome it," Senate Minority Leader Mitch McConnell, R-Ky., said Tuesday. "I told the president on Friday I hope he'll invite all of our members down for these dinners."
But other Republicans are refusing to give Obama the benefit of the doubt.
Fueling their reluctance is the not-so-distant memory of being hammered by the president on a near-daily basis amid last month's fight over the automatic spending cuts; Obama claimed Republicans alone were responsible for blocking a deal.
"All of a sudden there's a pivot literally overnight, where he wants to come to the caucus and everyone should get out the drums and pound them and sing songs," Rep. Greg Walden, R-Ore., who chairs the House GOP's campaign committee, said in an interview. "It doesn't work like that in any relationship I've been in."
White House aides say Obama is also sensitive to the fact that for Republicans looking ahead to the 2014 elections, appearing too chummy with a Democratic president could inflict more harm than good - especially for Republicans from conservative states who fear a primary challenge from their right.
A House leadership aide said that Speaker John Boehner, R-Ohio, believes Obama's outreach is genuine but that GOP leaders perceive it to be geared mostly toward boosting Obama's own standing. The aide was not authorized to discuss publicly internal GOP deliberations and spoke on condition of anonymity.
The White House argues it's the opposite. Freed from the need to run for re-election, aides said, Obama feels more flexibility to strike deals with Republicans that include provisions that liberals in his own party might not want, such as an adjustment for Social Security cost-of-living increases. Obama proposed the idea Tuesday in a meeting with Senate Democrats, but it's not included in the plan Senate Budget Committee Chairwoman Patty Murray, D-Wash., was to unveil Wednesday.
Murray's proposal would raise taxes by almost $1 trillion over a decade and cut spending by almost $1 trillion over the same period. But more than half of the combined deficit savings would be used to repeal the spending cuts that began to hit the economy on March 1 and are set to continue through the decade.
The president will release his own budget proposal in early April, although aides are playing down its significance because prospects that Congress will take up his plan are negligible.