In the Red Arrow diner, amid steaming plates of blueberry pie and fried bacon, Rudy Giuliani is grinning, signing baseballs and patting backs. He invokes Margaret Thatcher and Ronald Reagan, conservative heroes he would love to emulate.

“Their partnership brought down the Soviet Union,” the former New York Mayor shouts above the din. He then gets to the business at hand: reminding people of his heroic role after the September 11 terror attacks and his disdain for Hillary Clinton.

Amid all the machismo of this diner in New Hampshire, the crucial first primary voting state, Mr Giuliani knows that he is entering a critical phase of his campaign for the Republican presidential nomination. Some religious conservatives this week rebelled over his liberal views on abortion and gay marriage.

Peppered by questions about whether he can win the nomination as a pro-abortion candidate, Mr Giuliani said: “I cannot be all things to all people. If you disagree with me, don’t vote for me.” It was the clearest of signs that Mr Giuliani has decided to ignore social conservatives in the belief that their hold over the Republican nominating process is over.

The coming test of strength between Mr Giuliani and the Religious Right will determine if the power of social conservatives, the driving force behind the Republican resurgence of the 1990s, is waning.

Aides to Mr Giuliani believe that issues such as terrorism and Iraq - his greatest electoral strengths - are of more concern to many evangelicals and conservatives than abortion and gay marriage. The Religious Right is also in a state of flux, with a younger generation that wants to move on from the culture wars of the 1990s.

When the thrice-married Mr Giuliani announced his candidacy nine months ago, the conventional wisdom was that he stood little chance of being nominated.

His liberal views on social issues, and an erratic private life, put him at odds with the conservative Republican base, which has held enormous sway over the party’s primary process since the days of Ronald Reagan. But in new polls this week, Mr Giuliani has not only maintained the frontrunner status he has enjoyed since February, but increased it.

Nationally, he now leads his nearest rival, Fred Thompson, 34 per cent to 17. He is making ground in Iowa, and has moved into a statistical tie in New Hampshire with Mitt Romney, who enjoyed a double-digit lead there one month ago. He leads in South Carolina, where social conservatives hold particular sway. Even more intriguingly, he enjoys greater support among Republican evangelicals than any of his rivals.

Last night Mr Giuliani’s campaign team announced that he had raised $11 million (£5.3 million) between July and September, more than any of his Republican rivals, but less than half of the amount raised by Hillary Clinton.

Confronted with his surprising durability 90 days before the nominating process begins, some Christian conservative leaders threatened to defect and rally behind a third-party candidate if Mr Giuliani is nominated. The move indicated how worried social conservatives have become about their influence in the party.

They have cause for concern. Last November Rick Santorum, a darling of social conservatives, lost reelection to his Pennsylvania Senate seat in a landslide. Ballot initiatives opposing gay marriage and abortion were defeated across America. A recent Pew Research poll revealed a dramatic decline in support for conservative issues such as “traditional moral values”. Mr Giuliani’s message outside the Red Arrow was simple: he has the best chance to beat Hillary Clinton in a general election, and he has the strength and leadership to confront Islamic extremism. Polls support those contentions.

“Conservatives just want to keep Hillary out of office,” Frank Luntz, a Republican pollster, told The Times. “That helps Giuliani. And the battle against radical jihadism has become a social issue for conservatives. For many, September 11 has changed their priorities.” Mr Giuliani has also been helped by the lack of a clear conservative standard bearer. Mr Romney was pro-abortion as little as two years ago. Mr Thompson, a late entry, has seen his campaign falter. John McCain has never been trusted by the Right.

Mr Giuliani still faces big obstacles. But his chances of success will rest with Red Arrow diners like Barbara Charrette, a committed social conservative. “Issues like abortion have polarised the country. I’m looking for someone who is tough on terror, and a good administrator. Everyone is looking for the best person to beat Hillary. And that’s Rudy.”

Times Recommends

• Fish and chip shops ‘selling cobbler as cod’
• T in the Park festival at Kinross
• How to get Madonna’s Thighs