President Barack Obama is following through on his search for a “caucus of common sense” with that rarest of presidential commodities — his own time.

The president’s poor relationships with most rank-and-file congressional Republicans are well-known. He rarely calls lawmakers personally — something that was especially true in the past year and a half as he geared up for his re-election campaign.

But after spending weeks on an air war against the GOP and failing to get the party’s leadership to bend on the sequester, his tack changed after the March 1 deadline for automatic spending cuts hit.

In his news conference that day, Obama could find no fault in his own approach to getting a deal — infamously dismissing the idea that he could employ a “Jedi mind-meld” to get Republicans to budge. But he is now picking up the phone and calling them, and not just members of Republican leadership.

Obama in recent days has called a handful of rank-and-file Republicans, and Press Secretary Jay Carney has softened his own tone as the White House implores the GOP to compromise. “The president is interested in, you know, finding members of the caucus of common sense and working with them to bring about a resolution to this challenge,” Carney said. The president’s calls aren’t solely about the budget either — Carney noted Obama has also been reaching out on immigration and other pieces of his agenda.

But spending, the debt and the deficit are clearly job No. 1.

Sen. Susan Collins said her conversation with the president Monday was the first time that they’ve talked recently. “It’s long overdue,” the Maine Republican said of the president’s new outreach, suggesting Obama should have started more than a year ago.

She said she thinks there is a caucus of common sense ready to act if Obama keeps it up. “It certainly is, but we need the president to govern and to get out of campaign mode,” she said.

Collins wouldn’t detail the conversation beyond saying they talked about the budget challenges and John O. Brennan’s nomination to run the CIA. But Collins said she thought many in Congress have tremendous concern about Washington’s failure to take on the nation’s long-term budget problems.

“Even though it may be belated, at least the president does seem to be extending an olive branch,” she said.

As for the key question of whether revenue might be on the table in any budget deal, Collins said she wouldn’t prejudge what should be in a package. She noted that in the past she’s voted for getting rid of tax breaks such as those enjoyed by Big Oil companies. Collins said a key issue for her would be ensuring that tax revenue goes to deficit reduction, not more spending.

Obama also called Sen. Lindsey Graham, R-S.C., who recently offered up $600 billion in revenue as part of a grand bargain. Graham met last week with Obama and Sen. John McCain, R-Ariz., on immigration and other issues.

Graham held out hope Tuesday that a grand bargain could still occur.

“I think the president understands that the challenge for Republicans will be revenues and the challenge for Democrats will be entitlements. That’s the construct.”

And Graham praised Obama for reaching out to Republicans. “I think this is going to pay dividends for the country.”

Sen. Rob Portman, R-Ohio, who also spoke with Obama, said he’s still hopeful there will be an agreement on entitlements and tax revisions.

“I hope that it’s a sincere effort to take advantage of this window of opportunity between now and the end of the year,” he said.

Portman said the president needs to give political cover to his own party in order to get its support for major entitlement changes. “They won’t do it on their own,” he said.

As for revenue, Portman said, “we’ll have that discussion,” but he added that raising taxes would hurt the economy.

“On the one hand, Democrats are saying cuts are bad for the economy, and on the other side, they say they want tax hikes … that are definitely bad for the economy,” he said.

Obama also made recent calls to Sens. Tom Coburn, R-Okla., and Bob Corker, R-Tenn.

But there’s no guarantee Obama’s personal touch will move the needle on a deal.

Senate Minority Leader Mitch McConnell, R-Ky., said he expects the president to talk to senators. “Frankly, I wish he’d done more of that over the years. We’ve had, all of us, very limited interaction with the president,” he said.

Sen. Roy Blunt, R-Mo., who hasn’t gotten a call from the president, said the calls won’t net the president any more tax increases.

“I think that our conference and House Republicans are virtually united on the idea that the $1 trillion of new revenue in the president’s health care plan … and the $650 billion of revenue that he just got should be enough,” Blunt said.