President Barack Obama’s calls to about a half-dozen Republican senators to seek support for reducing the U.S. budget deficit represent the type of effort Republicans say has been lacking from the president.

Republican Senators Lindsey Graham of South Carolina and Susan Collins of Maine said they spoke with Obama today. Tom Coburn of Oklahoma, Rob Portman of Ohio and Bob Corker of Tennessee said they have received calls from the president since March 1, when Obama said he would speak with “a caucus of common sense on Capitol Hill” that he hoped would be open to a broad deficit-reduction deal.

“He just called me,” Graham told reporters as he headed into a closed-door Republican lunch today. The senator said the two spoke for about 10 minutes. “I’m very encouraged by what I see from the president in terms of substance and tone. He’s calling people - this is how you solve hard problems.”

The calls represent a shift in approach for Obama, who in fiscal talks with Republicans since 2011 has negotiated primarily with House Speaker John Boehner of Ohio and Senate Minority Leader Mitch McConnell of Kentucky. Rank-and-file Republican lawmakers have complained that Obama hasn’t tried to engage with them.

Graham, McCain

Last week, Obama met privately at the White House with Graham and Arizona Senator John McCain, the 2008 Republican presidential nominee. Republican Representative Scott Rigell of Virginia traveled aboard Air Force One to appear with Obama at an event in Rigell’s Hampton Roads district.

Graham said Obama was trying to “get more people in the mix” to back a deal to curb the growth in entitlement spending and rewrite the tax code.

“What I see from the president is probably the most encouraging engagement on a big issue that I’ve seen since the early years of his presidency,” Graham said. “He wants to do the big deal.”

McConnell said he didn’t view Obama’s calls to lawmakers as an end-run around Republican congressional leaders.

“He certainly doesn’t have to go through me to call my members, and I’m sure he will, and I encourage him to do so,” McConnell told reporters. “I wish he’d done more of that over the years.”

Collins said Obama left the impression “that he is sincere in wanting the two parties to come together.”

‘Real Falloff’

“He seems for the first time to be willing to exercise some political leadership on it,” she said. Collins said that early in Obama’s first term, he “regularly” called her, though “then there was a real fall-off in communication.”

White House press secretary Jay Carney told reporters today that Obama would continue calling lawmakers to try to build support for a plan to trim the deficit.

The White House is committed to “addressing entitlement reform in a very serious way” and rewriting the tax code, Carney said. He said both parties generally agree with those goals.

Asked whether Obama is seeking a so-called grand bargain in his talks with Republican lawmakers, Carney wouldn’t provide details about individual conversations.

Corker and Portman declined to give details about their conversations with the president other than to say they were optimistic that a broad deal is possible.

Debt Ceiling

Portman said he sees “a window of opportunity between now and the end of the summer,” when Congress is projected to again have to raise the federal debt ceiling.

“This is the last best chance to do the right thing,” Portman said.

Corker called his conversation with the president “constructive.” He said it was unclear whether a renewed effort to strike a grand bargain would gain any real traction.

“I don’t know - that’s the bottom line,” Corker said.

Republican Idaho Senator Mike Crapo said today in an interview that White House officials had contacted him to schedule a call with Obama. He was part of a bipartisan group known as the “Gang of Six” that worked unsuccessfully in 2011 and 2012 to craft a grand bargain for deficit reduction.

Crapo said he remains opposed to any revenue increase that doesn’t include a tax overhaul.

“We have to reform the tax code, rather than just look at some way to raise revenue in order to generate a greater foundation for more spending,” he said.

Coburn, another Republican member of the now-defunct bipartisan group, said he too received a call from Obama. While he remains open to working with Democrats on a deficit-reduction plan, the call “has not shaped” his perspective significantly, Coburn said.