President Obama tried giving in to Republican demands and got burned. Then he tried breaking Republicans, but it didn't work. Now, the president has embarked on a new strategy for dealing with Capitol Hill: killing them with kindness.

Obama this week dropped the cold shoulder he'd been giving Republicans in favor of a charm offensive, hoping to lay the foundation for an elusive grand bargain on taxes and entitlement spending and to ease tensions as he prepares to push immigration reform, gun control and climate change legislation sure to meet Republican resistance.

Obama was criticized in his first term by liberals for avoiding hot-button issues such as gun control, which would have faced stiff Republican resistance. During recent budget battles, he reversed course and waged a public campaign against the GOP -- with limited success. Now, he's adopting a middle ground, engaging with the very lawmakers he spent recent months skewering in talks over a long-term fiscal framework.

By Thursday, his new approach was on full display when he hosted Rep. Paul Ryan, R-Wis., an ideological foil and part of the 2012 Republican presidential ticket, for lunch at the White House.

"What he was doing wasn't working -- and it wasn't going to work," said Republican pollster Whit Ayres, of Obama's earlier approach to the GOP. "When you kick the people you have to work with, it generally doesn't go well."

Obama has focused primarily on Republican senators he believes could move to the political center. But in courting Ryan, Obama has targeted one of the Republican Party's major stars, a man who holds tremendous sway with staunch conservatives.

"I don't think he's looking to move many Republicans a long way, just a few Republicans a short way," said Republican consultant Tucker Eskew.

In recent days, Obama has spent more time and paid more attention to Republicans than at any other time in his tenure. He called them on the phone. He took key senators to a swanky dinner and picked up the tab. He agreed to make a rare visit to the Capitol to meet with them next week. And then he had Ryan, a fitness enthusiast, over to the White House for lentil vegetable soup and broiled sea bass.

Republicans said they appreciated Obama's latest efforts but expressed reservations about whether it was all for show or if the president would commit to specific, real spending cuts, particularly in entitlement programs. Obama said he's willing to tackle entitlement reform, but Republicans say he hasn't developed a proposal to do that.

"They can't be fantasy," Ayres explained. "The last time the president moved the goal posts. Republicans just don't trust him as a negotiator."

And simply playing nice is a far cry from reaching bipartisan consensus on issues that have confounded the parties, a reality White House officials acknowledged Thursday.

"We are not unrealistic in our expectations," said White House press secretary Jay Carney. "We are simply saying that it is the right thing to do ... to engage and have a conversation about these issues."

House Speaker John Boehner, R-Ohio, welcomed the outreach but issued a warning about the direction of the talks.

"If the president continues to insist on tax hikes," he said, "I don't think we're going to get very far."

And others see few downsides to Obama's charm offensive.

"It certainly can't hurt," quipped Democratic pollster Margie Omero. "It makes sense -- it's not like they could move further apart."