* Obama discusses deficit reduction with Paul Ryan
* Senate Republican notes "impasse" on taxes
* Tax reform, entitlements part of broad discussion
By Richard Cowan and Roberta Rampton
WASHINGTON, March 7 (Reuters) - U.S. President Barack Obama expanded his fledgling search for Republican allies on a possible deficit-reduction deal when he hosted lunch on Thursday for Paul Ryan, one of the House of Representatives' leading fiscal conservatives.
Coming the day after he took Republican Senators to dinner to discuss the budget, Obama's new outreach brought optimism that two years of fiscal battles could ease up. But the White House and Republican lawmakers signaled the road to a grand bargain will still be difficult.
Criticized for not forging links with the opposition, Obama has been unable to reach a long-term deal in often acrimonious talks with House Speaker John Boehner to trim at least $4 trillion in deficits over 10 years.
Obama's new tack seems to be in response to the failure of both sides to halt $85 billion in automatic spending cuts that kicked in last week. A Reuters/Ipsos poll on Tuesday showed Obama's approval rating falling to 43 percent, partly due to the partisan fight over taxes and spending.
Obama and his spokesman Jay Carney have frequently come under questioning from reporters about the president's unwillingness to speak to Republicans, who control the House.
Ohio Republican Boehner told reporters this week's thaw was "a hopeful sign. I think something will come of it."
On Thursday, Obama lunched at the White House on lentil vegetable soup and broiled sea bass with Ryan of Wisconsin, who spent much of last year bashing the Democratic president's fiscal policies when Ryan was the Republican vice presidential candidate. They were joined by Representative Chris Van Hollen of Maryland, the top Democrat on Ryan's House Budget Committee.
Obama told Ryan he wants to keep talking in the weeks ahead, the White House said.
While lawmakers and the White House have described the various meetings and conversations as productive, nobody was yet willing to predict success.
"We're not naive about the challenges that we still face," White House spokesman Carney told reporters.
And Republican Senator Ron Johnson of Wisconsin, a Tea Party favorite who dined with Obama on Wednesday, said, "There really is an impasse in terms of taxes and we just all recognize that."
Johnson said everyone at the dinner table agreed they had only four to six months to craft a major budget deal, which probably was not enough time to achieve comprehensive tax reform. The conservative senator said Obama wants to raise tax revenues purely through closing tax loopholes that benefit special interests. Republicans have been opposing any further tax increases for deficit reduction.
Johnson said Obama opened the dinner by discussing the financial problems facing Medicare.
Representative Ryan, having lost November's election to Obama and Vice President Joe Biden, has resumed his job as chairman of the budget panel, where he is in a position to chart his party's course on fiscal policy.
Next week, Ryan and his Senate Democratic counterpart, Patty Murray, will float competing budget blueprints for 2014 that could become a platform for Obama to negotiate an elusive "grand bargain" for significant deficit reduction over the next decade.
Meanwhile, Defense Department officials told Reuters Obama will not submit his fiscal 2014 budget blueprint to Congress until at least April 8 and that it might be less detailed than previous years' budgets.
In recent days, some prominent Republicans, including Senator Lindsey Graham of South Carolina and former Florida Governor Jeb Bush, have expressed an openness to tax increases to help control annual deficits contributing to a national debt that has skyrocketed to $16.7 trillion.
In return, the White House has signaled a willingness to find savings in "entitlement" programs including Medicare healthcare for the elderly and disabled. Democrats have long positioned themselves as protectors of these social safety net programs.
This week has seen a flurry of overtures from Obama, from phone calls to Senate Republicans to Wednesday's dinner at a fancy hotel restaurant near the White House, and Thursday's lunch at the White House.
Next week, Obama is expected to go to Capitol Hill for a rare lunch with all Senate Republicans - Maine lobster is on the menu - and to huddle separately with House members from both parties.
"The president is interested in finding out how wide that sentiment is" among Republicans in Congress for tax hikes in a deficit-reduction deal, said a senior Senate Democratic aide.
There are deep divisions in Congress over using new tax revenues to reduce the deficit. Boehner and Senate Republican leader Mitch McConnell of Kentucky, who both have to appease their party's conservatives, have been ruling out any new tax increases.
Boehner repeated that position on Thursday. "If the president continues to insist on tax hikes, I don't think we're going to get very far," he told a news conference.
Even as Obama and Republicans circle each other to gauge the willingness to make concessions on taxes and entitlement programs, some lawmakers involved in the talks stuck with long-held party positions.
Following the dinner, Republican Senator John Hoeven of North Dakota told Reuters the conversation centered around "how do we get to a big agreement in terms of the debt and deficit."
But later in the evening, Hoeven's office floated a statement from the freshman senator that held to an anti-tax stance. "When our economy grows and more people are working, we broaden our tax base and our revenues increase, without raising taxes. A rising tide lifts all boats," Hoeven said.
"That's not going to do it for Democrats," said the senior Senate Democratic aide.