Schwarzenegger, the Austrian-born California governor, drew on his own unique immigrant story to cast the GOP as a party of opportunity. "I want other people to get the same chances I did, the same opportunities," he said.
"And I believe they can. That's why I believe in this country, that's why I believe in this party and what's why I believe in this president,"to Republican delegates.
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Schwarzenegger preceded first lady Laura Bush as featured speakers on the second night of the Republican National Convention at Madison Square Garden.
"What a greeting! This is like winning an Oscar – as if I would know!" the governor said when he took the stage.
"You can count on him, especially in a crisis," said the first lady of her husband in prepared remarks.
Schwarzenegger and the first lady had their turns at the podium as 2,508 delegates formally bestowed their nomination on the president for a second term in office.
"Four more years," they chanted in unison after Pennsylvania, a crucial swing state in November, put Mr. Bush over the top. The sound system blared the song "Knock on Wood."
Compassion and diversity were the themes of the day as delegates on the convention floor brandished signs reading, "Viva Bush!" and "'W' Stands for Women!"
George P. Bush, whose father is Florida Gov. Jeb Bush and whose mother is from Mexico, said the Republican Party has "always represented the interests of all people seeking opportunity."
He told delegates that as president, his uncle has helped make home ownership a reality for more Americans and that more than half of minorities now own their own homes.
The president, locked in a tight re-election race, campaigned across three battleground states during the day and worked to extinguish a convention-week controversy of his own making.
"In this different kind of war, we may never sit down at a peace table. But make no mistake about it, we are winning, and we will win" the war on terror, he told an American Legion convention in Tennessee, one day after saying he didn't know whether victory would be possible.
"I probably needed to be more articulate," Mr. Bush conceded in a radio interview with conservative talk show host Rush Limbaugh.
Mr. Bush's Democratic rival, Sen. John Kerry, was at home in Nantucket, Mass., meeting with senior aides to discuss the shape of his fall campaign.
His running mate, Sen. John Edwards, accused Republicans of engineering an attack-driven convention.
"You know why? Because they don't have a plan to create jobs, to fix health care or to win the war on terror," said the North Carolina lawmaker.
The president was scheduled to introduce his wife Tuesday night, by satellite, from a campaign stop in Pennsylvania. The Bushes' 22-year-old twin daughters, Jenna and Barbara, were to address the delegates in Madison Square Garden just ahead of their father's live shot.
In her prepared remarks, Mrs. Bush said that her husband's leadership has helped 50 million men, women and children win freedom over the past four years, a reference to wars in Afghanistan and Iraq.
"I want to talk about the issue that I believe is most important for my own daughters, for all our families, and for our future: George's work to protect our country and defeat terror so that all children can grow up in a more peaceful world," she added.
Schwarzenegger, in a speech brimming with optimism, said, "America is back! Back from the attack on our homeland, back from the attack on our economy, back from that attack on our way of life. We're back because of the perseverance, character and leadership " of George W. Bush.
Schwarzenegger urged optimism about the country's economy, too.
"To those critics who are so pessimistic about our economy, I say: 'Don't be economic girlie men!'" Schwarzenegger said — a line from a Saturday Night Live spoof of him that he used against Democratic legislators earlier this year.
Schwarzenegger drew on his childhood in Soviet-occupied Austria to praise Mr. Bush's war on terror. "Terrorism is more insidious than communism," he said.
The president "knows you don't reason with terrorists. You defeat them. He knows you can't reason with people blinded by hate," he said.
Schwarzenegger never mentioned Kerry, with whom he is friendly, but he did get in some digs at the Democrats. "One of my movies was called 'True Lies,'" he said. "It's what the Democrats should have called their convention."
Schwarzenegger was the latest moderate Republican to take a prominent role at a convention nominating a far more conservative president. The governor and the president disagree on issues including abortion rights, which Schwarzenegger supports, and amending the Constitution to ban gay marriage, which he opposes.
In a contentious day in the streets around the convention hall, police made 260 arrests on a day of varied protests. Some activists donned pig snouts and rolled around in bogus $100 bills bearing an unflattering likeness of Vice President Dick Cheney.
Others demonstrated outside the offices of Fox News Channel, which they accused of a right-wing bias. Others protested near the site of the World Trade Center – Ground Zero in the terrorist attacks of Sept. 11, 2001.
More than 800 people have been arrested in convention-related protest activity since late last week, but the demonstrations have been largely peaceful.