WASHINGTON (Reuters) - Leading congressional Republicans said on Sunday a broad deal with President Barack Obama on deficit reduction and entitlement reform remains possible but differed over potential flexibility on taxes, with the House speaker and budget leader not bending.

The top Republican in Congress, House of Representatives Speaker John Boehner, and Budget Committee Chairman Paul Ryan also agreed with Obama's assessment that the United States was not currently in a debt crisis but that one was looming.

Boehner and Obama failed at the end of 2012 to hammer out a deal to get America's fiscal house in order but Boehner said he "absolutely" trusts Obama.

Ryan, his party's 2012 vice presidential nominee whose budget proposal last week was dismissed by Democrats, quoted former Republican President Ronald Reagan's 1980s view of dealing with the Soviet Union, saying that with Obama, he believes in the policy of "trust but verify."

Obama has engaged in a couple of weeks of outreach to Republican and Democratic lawmakers - some have called it a "charm offensive" - but the prospects of a large deficit reduction deal by midyear remained unclear.

Obama is advocating more tax increases on the wealthiest Americans coupled with new spending cuts to help curb deficits that have topped $1 trillion in each of the past four years.

Such a deal could include curbing spending on costly entitlement programs like the Social Security retirement program and the Medicare health insurance program for the elderly and disabled.

Speaking on "Fox News Sunday," Senator Bob Corker, a Tennessee Republican, said: "There, by the way, is a chance on a deal. I know the president is saying the right things. And we have an opportunity over the next four to five months."

Asked on ABC's "This Week" if chances for a "grand bargain" were dead, Boehner offered some hope: "I don't know whether we can come to a big agreement. If we do, it'll be between the two parties on Capitol Hill. Hopefully, we can go to conference on these budgets - and hope springs eternal in my mind."

Corker underscored the need for Democratic willingness on entitlement reform and signaled Republican flexibility on taxes.

"I think Republicans, if they saw true entitlement reform, would be glad to look at tax reform that generates additional revenue," Corker said. "And that doesn't mean increasing rates. That means closing loopholes. It also means arranging our tax system so that we have economic growth."

Boehner said if Obama "believes that we have to have more taxes from the American people, we're not going to get very far." Ryan called for "revenue neutral" tax reform without higher taxes.

Obama met last Wednesday with House Republicans and made little headway in persuading them to accept his demand for tax hikes as part of any deficit-reduction deal.

DEBT CRISIS

Obama said last week the country was not in a debt crisis and will be "in a sustainable place" for the next 10 years.

Boehner said while the United States does not have "an immediate debt crisis" one is looming because entitlement programs are not sustainable in their current form. Asked how long the country had to solve these problems, Boehner said, "It could be a year or two years, three years, four years."

Ryan added that "we do not have a debt crisis right now, but we see it coming." He noted the words of leading deficit hawk Erskine Bowles that America is the best-looking horse in the glue factory.

"America is still a step ahead of the European nations who are confronting a debt crisis, of Japan that's in its second lost decade," Ryan said.

Republicans and Democrats in Congress last Tuesday proposed vastly different plans to slash long-term deficits. On Thursday, a Senate bill to avert a federal government shutdown stalled under the weight of more than 100 proposed amendments as senators sought to attach pet provisions.

Senate Democratic leaders postponed further votes on the government spending legislation until Monday and said they would try to whittle down the number of amendments.

Dick Durbin, the No. 2 Senate Democrat, said on "Fox News Sunday" senators must pass the budget resolution "and then we're going to move to the next stage, and that is the grand bargain stage. That's what the president has tried to set up."

The Republican-controlled House last week passed a much less complicated version of the extension to government funding through September 30. Government agencies and programs face a broad shutdown if Congress fails to pass an extension by March 27.