The Republican National Convention spent a second night celebrating President Bush's leadership in the struggle against terrorism, praising him for putting "all his heart and soul" into the fight against America's enemies.

With first lady Laura Bush and California Gov. Arnold Schwarzenegger delivering emotional and highly personal speeches Tuesday night at Madison Square Garden, what had been billed by the convention planners as an evening devoted to Bush's 2000 theme of "compassionate conservatism" was preempted by the campaign's determination to keep the focus on Bush as commander in chief of the war against terrorism.

In an address that was lengthier and more revealing than any she had previously given, Laura Bush told a national television audience that "my husband didn't want to go to war, but he knew the safety and security of the world depended on it."

"I remember sitting in the window of the White House," she said, "watching as my husband walked on the lawn below . . . wrestling with those agonizing decisions that would have such profound consequences for so many lives and for the future of our world."

Schwarzenegger, the Austrian-born bodybuilder-turned-actor-turned-politician, called Bush "a man of perseverance, a man of inner strength, a leader who doesn't flinch, doesn't waver, does not back down."

The session opened as Bush tried to extricate himself from an incautious comment that the war on terrorism cannot be won. The president, who made the remark in a weekend interview with NBC, sought to cut off Democratic criticism of his statement by telling the American Legion convention in Nashville that while there may never be a peace treaty or surrender, "we are winning and will win."

The speeches by Laura Bush and Schwarzenegger far overshadowed those by Education Secretary Roderick R. Paige and Sens. Bill Frist (Tenn.) and Elizabeth Dole (N.C.). Those officials came forward to argue that Bush had fulfilled the compassionate conservatism promise of the last campaign by sponsoring major school and health care reforms -- and would do more in those areas if reelected.

A day of demonstrations called by anarchists and other activists ended with 600 arrests, as police chased protesters across Midtown Manhattan for more than five hours last night.

Picking up on the theme of Monday night's speakers, Sen. John McCain (Ariz.) and former New York mayor Rudolph W. Giuliani, Laura Bush said, "George's work to protect our country and defeat terror" is "the issue that I believe is most important for my own daughters, for all our families and for our future."

She credited her husband with making it possible for "50 million more men, women and children to live in freedom," praising especially the advances for some in Afghanistan and Iraq. Laura Bush said that Americans have learned in the past four years what she has learned as the president's wife. "He'll always tell you what he really thinks. You can count on him, especially in a crisis. His friends don't change -- and neither do his values. He has boundless energy and enthusiasm for his job and for life itself. He treats every person he meets with dignity and respect, the same dignity and respect he has for the office he holds.

"And he is a loving man, with a big heart. I've seen tears as he has hugged families who've lost loved ones. I've seen him return the salute of soldiers wounded in battle. And then, being George, he invites them to come visit us at the White House. And they've come, bringing an infectious spirit of uniquely American confidence that we are doing the right thing and that our future will be better because of our actions today."

The first lady was introduced on the stage by twin daughters Barbara and Jenna, who joked about life in the Bush family fishbowl. The president appeared via closed circuit from a campaign stop in Pennsylvania to say that the United States "would be fortunate to have her in the White House for four more years."

Schwarzenegger spoke to fellow immigrants, telling them they are "welcome in this party. We Republicans admire your ambition. We encourage your dreams. We believe in your future."

The governor became the first prominent convention speaker to directly address the economic issues that Democrats count as Bush's biggest political liabilities. Reprising a phrase he used -- controversially -- to describe California legislators, Schwarzenegger said: "To those critics who are so pessimistic about our economy, I say: Don't be economic girlie men." The delegates roared with approval.

"The U.S. economy remains the envy of the world," he said, adding that it is "moving ahead despite a recession they inherited and in spite of the attack on our homeland."

Without naming him, Schwarzenegger rebutted Sen. John Edwards's favorite line that there are "two Americas," one for the wealthy and one for everyone else. The Democratic vice presidential candidate uses it as shorthand for economic divisions, but Schwarzenegger said that the troops he has visited "do not believe there are two Americas. They believe we are one America and they are fighting for it. We are one America -- and President Bush is defending it with all his heart and soul."

Until Schwarzenegger spoke, the Republicans had used their prime-time access to a national TV audience without directly addressing the economic issues that voters say are as worrisome to them as the threat of terrorism.

Republican National Committee Chairman Ed Gillespie said in an interview that Vice President Cheney will speak on both the economy and terrorism on Wednesday night and Bush will defend his economic record on Thursday night -- along with his second-term plans to recoup the lost jobs and declining incomes that have marred his first term.

Edwards said in a statement that Republicans are avoiding economic issues "because they don't have a plan to create jobs, to fix health care or win the war on terror. And they certainly don't want to bring up the big elephant in the room -- 1.8 million jobs gone, more than 5 million people who have lost their health insurance, more than 4 million people who have fallen into poverty and American families who keep seeing their incomes drop year by year."

Last night, the Kerry-Edwards campaign announced a $45 million ad buy in 20 states -- the first stage in a media war that will begin after Labor Day.

Before the evening's speeches began, the convention completed the formality of nominating Bush for a second term, with Pennsylvania, a battleground state that went Democratic in 2000, given the honor of putting him over the top.

Dole and Sen. Sam Brownback (Kan.) combined their praise for Bush's efforts to combat AIDS and promote other social programs with the most explicit messages opposing abortion and same-sex marriage heard yet at the convention.

"Marriage is important," Dole said, "not because it is a convenient invention or the latest reality show. Marriage is important because it is the cornerstone of civilization, and the foundation of the family. Marriage between a man and a woman isn't something Republicans invented, but it is something Republicans will defend." The GOP platform calls for amending the Constitution to bar same-sex marriage.

Dole said that the same thing is true of "the right to worship God," adding that her party believes that Americans "are free to worship without discrimination, without intervention and even without activist judges trying to strip the name of God from the Pledge of Allegiance, from the money in our pockets, and from the walls of our courthouses."

Brownback said that because of "the mettle of George Bush," the United States is "leading the world in the heroic rescue of human life. This is the essence of compassionate conservatism," adding that "from the child in the womb to the mother carrying her, this nation and this president will fight for you."

Paige, a former Houston school superintendent, said Bush has "always had a compassionate vision for education: students challenged by high standards, teachers armed with proper resources, parents empowered with information and choices."

Rebutting Democratic criticism that the landmark No Child Left Behind Act passed by Congress in 2002 has been crippled by a lack of funding, Paige insisted the program is working. "All across America, test scores are rising, students are learning, the achievement gap is closing, teachers and principals are beaming with pride."

Paige was backed by George P. Bush, the president's nephew, who said the program opens the promise of the United States to every child, whether "new to our country or born in the heartland." Other speakers highlighted Bush's support for breast cancer research, adoption, faith-based and community service programs.

Frist, a physician as well as Senate majority leader, celebrated the passage of a Medicare prescription-drug benefit and criticized Democratic presidential nominee John F. Kerry for offering a health care plan that boils down to "take a handful of tax increases and 'Don't call me in the morning.' " Frist was particularly critical of Kerry and Edwards for opposing Republican legislation to limit awards for medical malpractice.

Before the evening session began, independent presidential candidate Ralph Nader was admitted to Madison Square Garden for a TV interview. The Associated Press quoted him as saying, "I like to observe corporate orgies."

Researcher Brian Faler contributed to this report.

In addressing the convention delegates, first lady Laura Bush says: "My husband didn't want to go to war, but he knew the safety and security of the world depended on it.""Republican cheerleaders" Todd Kolze and Yannis Cosmadopoulos perform at a Shut-Up-a-Thon to protest the Fox News station.George P. Bush, the president's nephew, says the No Child Left Behind Act opens the promise of America to every child.From left, Don Goldwater, Carmen Bermudez, Cindy Collins and Linda White enjoy the festivities at Madison Square Garden.Maria Shriver, left, and former president George H.W. Bush sit together on the second night of the convention, which featured Shriver's husband, California Gov. Arnold Schwarzenegger, as a speaker.