Wisconsin Gov. Scott Walker speaks during the North Carolina Republican Party convention in Raleigh, N.C., on June 5. (Gerry Broome/AP)

To build a war chest for his all-but-official presidential campaign, Wisconsin Gov. Scott Walker has been inviting wealthy prospective donors here for a series of private, leisurely dinners — 10 to 20 people at a time — at the top of the Edgewater, a luxury hotel with sweeping views of this capital city.

He tells the crowds that he is a “winner” and a “fighter” with a unique ability to unite the disparate wings of the Republican Party. The reception has been warm, and the checks have rolled in.

But the reaction to Walker’s likely candidacy has been cooler in another key city, New York, where he has struggled to make inroads among the powerful and monied financial community — in part because of his strident opposition to same-sex marriage and his positions on other social issues. One billionaire hedge fund manager got into a long argument with Walker over same-sex marriage and then pulled his support because of it, said a Republican familiar with the meeting.

The contrast highlights the central challenge Walker faces as he prepares to formally begin his campaign next month: how to expand his aw-shucks, socially conservative Midwestern appeal to the broader Republican Party and to the rest of the country. He already has stumbled several times because of his tendency to make off-the-cuff comments that quickly need clarification. And although he has successfully fought Democrats and unions in Wisconsin, running for president would mean battling fellow Republicans — including some with more money and more experience on the national stage.

His allies, however, say he is off to a strong start. Walker is at the front of the crowded GOP field in early polls. He is stockpiling money in a new political committee and quietly assembling a staff and advisers in Iowa and other early primary states. Donors have given or promised at least $20 million to various pro-Walker fundraising groups, including an allied super PAC, said three Walker allies with inside knowledge of the fundraising operation.

Scott Walker, governor of Wisconsin, arrives to speak during the inaugural Roast and Ride in Boone, Iowa, on June 6. The Iowa caucuses will be central to Walker’s likely 2016 bid. (Daniel Acker/Bloomberg News)

“You have the Republican Party being depicted as out of touch, as the party of the rich,” said Chart Westcott, a Dallas-based biotech investor. “Then here comes this guy who shops at Kohl’s and rides a Harley — an all-American, really likable guy. That’s what makes Walker unique. He is the most normal human being to run for president in a very long time.”

Walker’s strategy, which he has laid out in interviews and at donor events, is straightforward: win the Iowa caucuses and then perform well in the New Hampshire and South Carolina primaries. In Florida, let former governor Jeb Bush and Sen. Marco Rubio blow through tens of millions of dollars fighting each other in their home state. Scoop up delegates in the Southern and Midwestern states that come next. And through it all, raise enough money to stay at the front of the pack.

“Having been up to New Hampshire a bunch, having been in South Carolina and Iowa . . . voters want more than just ads. They want to talk to you,” Walker said in a recent interview with conservative radio host Howie Carr. “You can have all the money in the world, but if your message isn’t connecting, I think at some point large sums of money become a disadvantage.”

Unlike most governors, Walker has his own national donor database. In 2012, he faced a recall election after stripping many unions of their bargaining rights. That contest, along with his reelection campaign in November, attracted the attention of conservative benefactors nationwide who relished his win over organized labor.

By January, Walker was focused on his next possible race. He launched a tax-exempt political organization, Our American Revival, that can accept unlimited donations and has funded his near-constant travel around the country. In April, two of his longtime aides started a super PAC, the Unintimidated PAC, that also can collect and spend unlimited amounts of money. (The PAC is named after Walker’s 2013 biography, “Unintimidated: A Governor’s Story and a Nation’s Challenge.”)

Walker circled back to donors who showed interest in his gubernatorial races and tried to convince them that he could do the same thing at the national level. At least a dozen leisurely dinners were held at the Edgewater, usually for about two dozen guests, plus similar dinner parties throughout the country, including one at the New York apartment of TD Ameritrade founder Joe Ricketts.

Walker has gained the support of heavyweight backers who could give him substantially more as the race heats up, including Todd Ricketts (Joe’s son and co-owner of the Chicago Cubs), real estate developer Leonard Stern and hedge fund billionaire John Paulson, who wrote the super PAC a $100,000 check.

Scott Walker arrives at Big Barn Harley Davidson in Des Moines on June 6. Walker’s Harley ownership is part of his potential appeal as an everyman presidential candidate. (Daniel Acker/Bloomberg News)

With donations and promises totaling $20 million, Walker allies hope to have at least $15 million on hand by the end of the month. Overall, Walker is aiming to raise $30 million to $40 million by primary season next year, allies said.

The goal is not to match Bush, whose super PAC had aimed to collect at least $100 million by the end of June. Instead, Walker’s supporters say they want to keep pace with Rubio and Sen. Ted Cruz (Tex.).

“What we’ve learned in politics is that the ideas matter more than money,” said Anthony Scaramucci, a New York investor and former Mitt Romney fundraiser who has a senior role in the Walker operation. “He will be the entrepreneurial candidate, tight and lean, figuring out how to do more with less.”

Lately, Walker has begun headlining bigger donor events. More than 100 people gathered at Todd Ricketts’s home outside Chicago in late May for a barbecue, complete with cheeseburgers and beer. In early June in North Carolina, Walker spoke at a luncheon for 250 in the back yard of Garland S. Tucker III, the chief executive of a Raleigh investment company.

“The fact he has run and governed as a conservative in a pretty blue state made me think that he’s the kind of candidate who can not only unite the Republican Party but pull in some independents,” said Tucker, who has made a “fairly substantial” donation to the super PAC.

Before that lunch, Walker met privately with about 30 high-capacity donors, including North Carolina retail magnate Art Pope, a major conservative benefactor with strong ties to billionaire brothers Charles and David Koch.

“He’s not the most charismatic speaker, but I don’t think people are looking for the most charismatic,” said Pope, who said that he has not chosen a 2016 favorite but said he is seriously considering Walker. “They are looking for the best candidate who would do the best job governing, not the best stump speech.”

The same-sex marriage issue has caused Walker problems among some donor groups, however, particularly Republicans in New York.

“Sometimes you can say something and people think you don’t mean it, and sometimes you can say something and people think you mean it,” said one Republican who has seen this tension play out. “When Barack Obama said he’s against gay marriage in 2008, people didn’t think he meant it. But when Scott says it, people think he means it. This is a very big stumbling block for him on Wall Street.”

Walker, the son of a Baptist preacher, said earlier this month that he would support a constitutional amendment allowing states to ban same-sex marriage. Those close to Walker have played down the role of this issue and say he will not change his beliefs to appease donors.

Walker took another step toward a formal launch last week with the formation of a “testing-the-waters” committee, asking donors to raise $27,000 by the time of his expected announcement July 13.

Walker has been traveling nearly constantly, including trips to Europe, Israel and Canada that have garnered criticism from Democrats back home. On the stump, his confident riff about “fighters” and “winners” has become a regular routine.

In a speech this month at a donor retreat hosted by Romney, Walker said senators in the race have fought Democrats but “have yet to win anything or accomplish anything.” And current and former governors are good at winning reelection, he said, “but they have yet to take on the really big fights.”

“We’ve done both,” Walker continued. “We have fought the good fights over and over and over again, and we have won those fights.”

Gold and Rucker reported from Washington.