The Republican Party’s long search for a standard-bearer is placing extraordinary pressure on the tough-talking governor of New Jersey to suddenly leap into a presidential race that he has long denied interest in entering.

As the clamor reached a heightened pitch, Gov. Chris Christie arrived Tuesday night at the symbolic heart of political conservatism, the Ronald Reagan Presidential Library, to deliver a speech on American exceptionalism that some Republicans had hoped would be the opening stroke of a presidential campaign.

Christie gave an impassioned call for strong leadership, accusing Washington of drifting from crisis to crisis without resolution and President Obama of being a “bystander in the Oval Office.” In his nearly 30-minute speech, Christie offered no indication he might offer himself as that strong leader, but didn’t close the door, either.

During an audience question-and-answer session, a woman stood up and pleaded. “I really implore you — I really do. This isn’t funny. I mean this with all my heart,” she said. “Please, sir, reconsider. Go home and really think about it. Please. Do it for my daughter, do it for our grandchildren, do it for our sons. Please, sir, your country needs you to run for president.”

The audience rose to applause and Christie, in an emotional moment, responded: “I feel the passion with which you say it, and it touches me.”

The governor said he was listening to those urging him to run, adding that he was taking it in and “feeling it too.” But he continued, “by the same token, that heartfelt message you gave me is also not a reason for me to do it. That reason has to reside inside me. That’s what I’ve said all along. I know without ever having met President Reagan that he must’ve felt deeply in his heart that he was called to that moment to lead our country. And so my answer to you is just this, I thank you for what you’re saying.”

With that, Christie ensured the speculation would go on.

Even with no apparent campaign in the offing, Christie summoned the nation’s political leadership to take action and lead through compromise. “When there is a problem, you fix it,” he said. “That’s what you do. That’s what we did. That’s the job we’ve been sent to do. And you cannot wait for someone else to do it when you’re sitting in the Oval Office.”

Christie arrived at Simi Valley, Calif., surrounded by a buzz of which most politicians could only dream. For a month, and especially this past week, a growing chorus of Republican contributors, commentators and activists have ramped up calls on him to run for president. Over and over, they told Christie that this is his moment and his country needs him.

But the pressure may say less about Christie’s potential as a candidate than it does about the unease many Republicans have with the current presidential field.

“The Republican Party is a party that believes in the power of markets and the free enterprise system, and what you’re seeing here is a market where there is demand for an additional candidate in the race,” said Steve Schmidt, who was John McCain’s top strategist in 2008 and is unaligned this time. “There is a whole class of Republican donors and activists who aren’t done dating yet. They’re not ready to put a ring on anyone’s finger.”

Since missing his shot at the nomination in 2008, Mitt Romney has stood ready to take the baton. But the party has been unwilling to hand it to him. While the former Massachusetts governor is an improved candidate, he may never be loved by the conservative core of the GOP. Romney might end up as its nominee, but he doesn’t excite the activists.

Republicans are confident that they have a golden opportunity to deny President Obama a second term in 2012. The nation’s sputtering economy and the American people’s growing unease with Obama’s leadership tell them that. But the GOP is in a different place than it was even a couple of years ago, and it has not settled on what that place is nor what kind of leader would best reflect it.

Texas Gov. Rick Perry was thought to be that person. Here was a big leader who had governed a big state, with a record of accomplishment in overseeing job growth during the recession. But although his hopes are far from dashed, Perry has disappointed some influential conservatives with a series of unsteady debate performances and with positions on immigration more moderate than those of the party’s base.

Perry’s missteps have raised demand in some corners of the party for another candidate. Enter Christie, whose supporters have long championed his potential as a national candidate despite his repeated insistence that he has no interest in running for president. In Christie, some Republicans see a unique politician who they believe can take the fight to Obama.

“He has been extraordinarily effective as governor of New Jersey, he has done exactly what he said he was going to do and he stands apart from many politicians in terms of telling people what he believes as opposed to what he thinks they want to hear,” Schmidt said. “People are responding to that leadership.”

Republican strategist Karl Rove, appearing on Fox News Channel moments before Christie’s speech, called the governor the “everyman of American politics.”

“He’s clearly got the capacity to jump into this race and contest it,” Rove said.

But if Christie runs, there’s no guarantee that he’ll end up fulfilling all the dreams of his benefactors. Politicians often look better on paper than they do once they begin to campaign beneath the presidential spotlight and face the scrutiny all that entails.

Christie, 49, became governor, his first elected office, in 2010 after seven years as U.S. attorney. Despite his national profile as a budget-cutter who is tough on labor unions, he has taken some positions, including support for civil unions and a path to citizenship for illegal immigrants, that may not sit well with the conservative base.

In recent days, a tremendous number of calls have come into Christie and his political advisers in Trenton, N.J. Christie’s more fervent boosters reportedly include a roster of prominent businessmen: Kenneth G. Langone, the founder of Home Depot; David H. Koch, the tea party benefactor; and financiers Paul E. Singer and Stanley F. Druckenmiller. Vocal support also has come from leading conservative commentators, including William Kristol, editor of the Weekly Standard.

They have been telling Christie that this is his moment, and the governor has done little to quiet their clamor. His office has issued soft denials, but some Republicans close to Christie said he was seriously considering jumping into the race. One of them, former governor Tom Kean, told the National Review: “It’s real. He’s giving it a lot of thought.”

Christie’s speech at the Reagan library and a fundraising trip through Missouri, California and Louisiana this week added to the speculation that he might run — even though his schedule had been set for weeks and he agreed to give the speech at the library after a personal invitation from Nancy Reagan.

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