WASHINGTON » At the climax of each of the fiscal crises that have paralyzed the nation’s capital since the Republican landslide of 2010, Sen. Mitch McConnell, the wily Kentuckian who leads the Senate Republicans, has stepped in to untangle the seemingly hopeless knots threatening the economy.

But as Congress trudges toward its next budget showdown, the Mr. Fix-It of Washington is looking more like its Invisible Man as he balances his leadership imperatives with his re-election.

"The House and the White House in the end will have to reach some kind of understanding on both these issues," McConnell said last week as he sat in his spacious Capitol office and looked toward Sept. 30, when much of the federal government runs out of money, and mid-October, when it exhausts its borrowing authority. "I don’t intend to participate in any discussion, publicly or privately, that raises taxes or spends more than current law."

That may prove to be more threat than destiny. The taciturn lawmaker is known for playing his cards extremely close to his vest, and when he has swooped in to resolve impasses, he has usually come in late — more a closer than a middle reliever. But his decision to stay out of the budget fray is one of the central reasons a resolution seems distant at the moment.

Democrats and, increasingly, Republicans are complaining that the minority leader’s absence from many of this year’s most intense and consequential negotiations — from the immigration overhaul to the budget to a fight over internal rule changes that almost paralyzed the Senate — has created a power vacuum and left Democrats without a bargaining partner.

They worry that McConnell is too hamstrung by political concerns in the Capitol and back home in Kentucky. In Washington, a rebellious crop of new Republican senators, led by Ted Cruz of Texas, has rejected his compromising brand of politics. Cruz has led the charge to tie any further government financing to gutting President Barack Obama’s health care law, a movement that has angered many veteran Republicans and brought the federal government to the brink of a shutdown.

On Monday, McConnell gave the first indication of how he will figure into the budget standoff, saying that he would support a House bill that denies financing for the health care law, putting him at odds with Cruz, who has encouraged his colleagues to filibuster the bill so Democrats cannot amend it.

And in Kentucky, the junior senator, Rand Paul, has largely set the agenda for a Tea Party-infused Republican Party there.

McConnell is dealing with an unwanted primary challenge from a well-financed Tea Party candidate who keeps telling Kentucky voters the senator is an establishment pawn.

McConnell is leading his challenger by a large margin in internal polls. But after Tea Party candidates rose from nowhere in the past two elections to beat veteran senators, McConnell is leaving nothing to chance.

"He’s got an election," said Sen. Harry Reid of Nevada, the majority leader. "And that’s his No. 1 concern. I hope we can work together on things, but we’ll just have to wait and see."

What worries members of both parties is that efforts to work around McConnell and bridge the partisan disagreements over the budget, health care and taxes have failed.

Early this year, just off his re-election triumph, Obama tried to reach out to Senate Republicans beyond the leadership. This group, called the "sounding board," met repeatedly with the White House chief of staff, Denis McDonough, and other senior White House officials and came away with nothing.

Sen. Lindsey Graham, R.-S.C. and a member of that group, said what was lacking was the level of trust that would persuade the two sides to accept a deal that would be politically difficult for both sides’ most dedicated activists to swallow. He said that Vice President Joe Biden and McConnell trusted each other. No other partners have emerged in McConnell’s absence to fill "probably the biggest missing ingredient," Graham said.

Not one to enjoy small talk, McConnell rarely speaks at length during meetings. But his presence has become so spectral that some Democrats have taken to referring to him as "the man who isn’t there."

For example, during a meeting this month with all four leaders of the two chambers — Speaker John A. Boehner, Reid, McConnell and Rep. Nancy Pelosi, the House minority leader — he seemed so disengaged from the conversation, one Democrat briefed on the meeting said, that Reid later remarked how few words his sometimes-adversary had said.

And in late July, when the two Senate leaders tried to resume regular meetings in hopes of repairing their relationship after a bruising fight over changing Senate rules to make it harder for Republicans to block the president’s nominees, Reid made a similar observation to colleagues. He said he was taken aback by how absent McConnell seemed.

They have not met privately since Congress returned from its summer recess, despite the serious issues crowding the Senate’s agenda, from Syria to the budget, though they have spoken on the phone.

The current crisis had its origins at a meeting of Republican senators in July, where Cruz and Sen. Mike Lee of Utah presented their plan to urge their colleagues to vote against any budget that provides money for the president’s health care law – in effect threatening a government shutdown.

They said they had written a letter outlining their position and were recruiting signatories. For those who refused to sign, they offered an alternative: Come up with your own plan.

McConnell’s response was noncommittal. He said, according to a Republican aide, that he was waiting to see what budget the House would pass. He has not signed the letter despite pressure from the right to do so. "It creates a situation where senators like Mike Lee and Ted Cruz become the leaders," said the Republican aide, who spoke on the condition of anonymity to discuss meetings that senators are discouraged from talking about publicly.

With his re-election campaign building steam, his voting record has veered from the mainstream of Republican politics. His newfound affinity for issues like legalizing hemp farming and protecting the United States from government drones seems to grow more from a partnership with Paul than his own legislative history.

In an interview Thursday, McConnell said he remains proud of his deal-brokering accomplishments – which included hatching a plan to work around the Tea Party in 2011 that allowed the debt ceiling to be raised without an affirmative vote, and sealing a compromise with Biden last December that averted the "fiscal cliff" – even if he now sees little purpose in rolling up his sleeves.

"Those were deals that in my view were worth negotiating because they produced permanent tax relief, and permanent spending reductions," he said. "I don’t see any circumstances or any hints, any indications whatsoever, that this Senate or this president is willing to do anything other than to try to unravel what we already achieved."

Such caution may recede as the Kentucky Senate race settles in. McConnell aides say confidently that their internal polls show them with a wide lead over the Tea Party challenger, Matt Bevin. His supporters circulated a video last week of Bevin, a businessman and self-described "constitutionalist," confusing Article Five of the Constitution with the Fifth Amendment to the Constitution.

Some say they still believe that McConnell will ride to the rescue in budget negotiations, even if he ultimately cannot vote for the deal he helps midwife.

"In the final analysis, Senator McConnell’s going to be right in there," said Sen. John Hoeven, R-N.D.

Aides noted that McConnell ultimately helped broker the bailout of Wall Street in 2008, just weeks before his last re-election campaign came to an end. But in 2008, of course, there was far greater tolerance from the right for the compromise politics that McConnell has perfected.

"I think what’s changed isn’t Mitch McConnell," said Sen. Marco Rubio, R-Fla., who was elected in the Tea Party wave of 2010. "What’s changed in general is the nature of American politics."

"The grass-roots have more influence over the political process than they ever have, and I think that’s a positive development," he added. "You know, there was a time around here not so long ago where people could sneak all kinds of things into a bill, where members could vote any way they wanted and no one would ever find out."

"Now you can’t do that."

© 2013 The New York Times Company