U.S. Senate candidate Chris Murphy stood in a chilly, wind-blown parking lot Saturday, listening to Congressman John B. Larson and the presidents of two national public-employee unions exhort dozens of volunteers about to go door-to-door in Hartford on behalf of him and other Democrats.

The scene would be repeated throughout the weekend.

Murphy’s fate on Tuesday is intertwined with that of President Obama, candidates for Congress and the General Assembly, ward leaders in New Haven, organized labor and the rest of a Democratic coalition he needs to overcome his campaign’s limitations and his opponent’s resources.

Linda McMahon’s success or failure will be hers alone.

McMahon has helped the GOP raise money, but her campaign is McMahon, Inc., independent of the Republican Party. It has its own network of 13 field offices, more than 100 paid staffers and thousands of volunteers organized at a cost of nearly $96 million over the course of back-to-back campaigns for two open Senate seats.

Last week, McMahon wrote her campaign checks for $1.3 million and $3.3 million, a $4.6 million infusion of cash over two days equal to about half the $9.3 million raised by Murphy since he became a candidate. As of Oct. 26, according to federal election records, she had loaned or given her campaign $44.6 million.

“It is an extraordinary campaign, unprecedented,” said Jerry Labriola, the GOP state chairman. “The scope of it is without any precedent. They are going to have a terrific ground game, and the entire ticket will benefit.”

The next highest self-funder this year is David H. Dewhurst, a Republican who has spent $20.4 million on a Senate campaign in Texas.

Democratic organizers concede that McMahon has spent $46 million more effectively in 2012 than she did $50 million in 2010, paying closer attention to the less glamorous aspects of campaigning: Building a machine that can identify supporters and deliver them to the polls.

“All the Democrats, I told, ‘Be wary of her. She’s buying a grass-roots organization,’ ” said John W. Olsen, president of the Connecticut AFL-CIO. “She went out, she invested, she put her time into that. She did a good job of putting that kind of stuff together.”

Evidence of McMahon’s ground game was in her early spending reports: payroll expenses approaching $2 million, mileage reimbursements of $100,000, office rents of $200,000 and $63,000 to keep everyone connected by cell phone. She relies on the GOP for no mail or materials. Final totals will be much higher.

Overall, she is on track to outspend Murphy, 5-1.

Murphy joked about McMahon’s resources Saturday, standing in the cold in a parking lot outside the Hartford Federation of Teachers, a few blocks from the state Capitol, where volunteers came to pick up door-knocking assignments, preceded by a brief rally.

“She would probably have each of you with a personal space heater, paid for by the McMahon campaign, to keep you warm,” Murphy told the volunteers, who sipped union-supplied Dunkin’ Donuts coffee. “All we’ve got is each other here, but you know what, that’s all that matters, right?”

The national significance of the Connecticut Senate race was underscored by the presence of two national union leaders: Lee Saunders, the president of AFSCME, and Randi Weingarten, the president of the American Federation of Teachers. Both mentioned Hurricane Sandy,

“In some ways the tragedy of Sandy brings into sharp relief what this election is about. This week, we are all in it together. We can’t be alone. This week, it is clear as this day is cold, that we need to have a government that works for the people,” Weingarten said. “We can’t do it alone. None of us in this parking lot can do it alone.”

The coordinated campaign

The Democratic counter to McMahon’s resources is the coordinated campaign, an interlocking series of efforts that stretch from the White House, where Obama recorded a commercial for Murphy, to local precincts like the 29^th Ward of New Haven, where the ward chairperson, Audrey Tyson, is tending to business like the distribution of 90 absentee ballots in an elderly housing complex.

Murphy campaigned in Tyson’s ward Friday.

“We understand it’s got to be a coordinated effort,” said U.S. Rep. Rosa L. DeLauro, D-3^rd District, the dean of the delegation and a resident of New Haven, the city that produced a plurality of more than 18,000 votes for Democrat Richard Blumenthal in the 2010 Senate race. “This time, we’re going to be in the 20s.”

DeLauro watched Murphy address an audience of older voters in the basement of Park Ridge, a seniors’ complex. The invitations went out from Tyson, the pizza and pastry was bought by DeLauro’s campaign. Murphy arrived with Ted Kennedy Jr. of Branford, the son of the late senator.

On a counter next to the food were two glossy cards. One, paid for by the Connecticut Democratic Party, said,  “When you vote for President Obama, vote Chris Murphy.” The other, paid for the New Haven Democratic Town Committee, urged a party line vote for Obama, Murphy, DeLauro and two local state legislative candidates. It offered rides to the polls.

By design or happenstance, Republicans are not opposing any member of the New Haven delegation to the state legislature, meaning that Democrats passed up public financing that would have brought hundreds of thousands of dollars of campaign funds into the city.

It also is an invitation to Democratic legislators to slack off.

But state Senate Majority Leader Martin M. Looney, D-New Haven, said the entire delegation was working for Murphy and the rest of the ticket. All were expected to attend a canvassing kickoff Sunday with Murphy and DeLauro.

Crucial city vote

Turnout in the cities and inner suburbs is crucial to Murphy. His campaign stops Saturday and Sunday brought him to some of the places that produced significant pluralities in 2010 for Blumenthal over McMahon: Hartford, 14,000; Bridgeport, 13,000; Hamden, 7,000; New Britain, 6,000; and, of course, New Haven.

It is easier for Democrats to coordinate their efforts, because the top of the ticket, Obama, is an asset to the rest of the ticket in this blue state, where the president is expected to outpoll Mitt  Romney by at least a dozen percentage points.

The national GOP brand is a detriment to McMahon, who produced a TV commercial appealing directly to Obama voters. Both McMahon and Andrew Roraback, the Republican candidate for the open seat in the 5^th Congressional District, sell themselves as independent-minded candidates.

“I think people in Connecticut are through with electing Republicans to national office,” Murphy said. “I just think the Republican Party nationally has abandoned Republicans here in Connecticut.”

Unlike Murphy, who can mine the cities for votes, McMahon’s campaign has to pull its votes from across the state in populous suburbs like Cheshire, Fairfield and Glastonbury, where she either broke even or won by narrow margins in her 2010 bid for the Senate, and in the smaller towns.

So her campaign is everywhere, a boost to a Republican Party that cannot otherwise match the resources of the Democratic coalition. Democrats outnumber Republicans in party registration, and they hold every statewide and congressional office and nearly two-thirds of the seats in the General Assembly.

But where the Democrats are jointly running phone banks from shared offices, McMahon’s phone canvassers ask about McMahon, not the rest of the GOP ticket. In Torrington, for example, Democrat Elizabeth Esty’s congressional campaign in the 5th District works in a shared office with other Democrats. Roraback and McMahon have their own offices, on the same street.

Corry Bliss, the manager of McMahon’s campaign, said her working relationship with other GOP candidates is good.

“I think the tremendous ground game we’ve put together over the past year, which will end up making in excess of 800,000 door knocks and well over a million phone calls, is really going to help candidates who are running for state House and state Senate,” Bliss said.

Republicans are grateful, if wary. Their gubernatorial nominee, Tom Foley, self-funded his losing campaign in 2010, as did McMahon. Two other self-funders, Mark Greenberg and Lisa Wilson-Foley, failed to win a GOP primary for an open congressional seat in the 5^th District.

The leader of the Republican minority in the state House of Representatives, Rep. Lawrence F. Cafero Jr. of Norwalk, who has tried to build his caucus into an organization that recruits and supports candidates, said McMahon clearly has been an asset to the party.

“I think everybody is appreciative of the resources she has put into this election for herself and, also, how she’s established quite a ground game,” Cafero said.

But he said the party needs a broad and permanent infrastructure, starting with local town committees.

“If any one party is reliant on one entity for future races, I think you are in trouble,” Cafero said. “I don’t think the Republican Party is reliant on Linda’s infrastructure, whether she wins or loses.”