Cheney will contrast Mr. Bush's "demonstrated leadership and decisiveness versus Senator Kerry's confusion of conviction – both in foreign and domestic policy – that he's demonstrated during his 20 years in the Senate," Cheney spokeswoman Anne Womack said.
Cheney also plans to discuss the importance of public schools, a vibrant economy and improved health care system, Womack said, and will argue that these things are not possible unless the nation is safe and secure.
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Before Cheney speaks, a Democrat, Sen. Zell Miller of Georgia, will deliver the convention's keynote address.
Miller was expected to talk about Mr. Bush's agenda for creating jobs and encouraging people to own homes and start businesses.
Miller said he would "explain to them why this longtime Democrat, who has never voted for a Republican, by the way, in his life, is voting for this one. And it has to do with the kind of man he is."
Mr. Bush was to arrive in New York late Wednesday for a meeting with firefighters, making the connection to the Sept. 11 attacks and subsequent fight against terrorism that has defined his presidency.
Kerry was in Nashville, Tenn., on Wednesday speaking to the same American Legion gathering that Mr. Bush addressed the day before. Noting that the president said earlier in the week that the terror war could not be won, Kerry said, "With the right policies, this is a war we can win."
In a television interview that aired Monday, Mr. Bush said the terror war couldn't be won. He amended the comment in his speech to the American Legion, saying it could be won.
Kerry's appearance broke a tradition in which presidential candidates have refrained from campaigning during the other party's convention. He used the occasion to again criticize Mr. Bush's Iraq policy.
"I would never have gone to war without a plan to win the peace," Kerry said.
In New York,as thousands of people waving pink slips formed a line three miles long to protest the Bush administration's economic policies.
A small group of AIDS activists managed to penetrate Madison Square Garden itself, although the convention was not in session at the time. They blew whistles and chanted, "Bush kills," at a morning session of GOP youth before being hustled from the floor.
Police said convention-related arrest over the past week now totaled more than 1,700.
As Wednesday night's program got underway, Republican delegates wrapped up the traditional roll call of the states, making President Bush their unanimous choice to lead their ticket in November.
The announcement brought a brief celebration on the convention floor – too brief for convention co-chair Michael Steele, Maryland's lieutenant governor.
He appealed to delegates, saying, "We can do better than that." He urged them to "bring it home for the president."
They responded with several minutes of cheering and the waving of signs reading, "Four more years" and "W, the president."
Delegates then made official Dick Cheney's nomination for a second term as vice president.
With two months remaining in a close election, and the pool of undecided voters a small one, Republicans relished the opportunity to place a Democrat out front at their convention. They had their man in Miller, a conservative ex-Marine who minces no words and delivered a keynote address a dozen years ago in the same hall in service of Democrat Bill Clinton.
While Democrats are peeved at Miller for his speaking role, they plan to focus most of their criticism on Cheney.
"When Dick Cheney takes the stage at the convention, we will be reminding Americans about Dick Cheney's record, not only his abysmal failure as vice president but the sweetheart deals that his administration has cut with the company that he used to lead," said Matt Bennett, a spokesman for the Democrats. Halliburton, the company that was headed by Cheney before he became Mr. Bush's running mate, has a multibillion-dollar contract for work done in Iraq.
On Wednesday, Cheney's wife, Lynne, defended her husband, saying he's been an asset to Mr. Bush.
"I think Dick has, you know, brought just a world of expertise to this job, which he really didn't plan on having, but has enjoyed greatly," Mrs. Cheney told CBS' The Early Show. "I think the president values his advice, and, in the end, I suspect that's the most important audience."
Cheney, 63, who served in President George H.W. Bush's administration as defense secretary, has seen his approval ratings plummet amid persistent questions about his role in promoting the Iraq war and in handling the Sept. 11 terror attacks.
But Mr. Bush has stuck fast by him, even as a new CNN/USA Today/Gallop poll conducted last week showed that 52 percent of those surveyed said they would vote for Democrat John Edwards for vice president over Cheney, if they could select the vice president separately.
Asked whether Cheney had given Mr. Bush good advice or bad advice over the past four years, 41 percent answered "good advice," 39 percent answered "bad advice" and 17 percent said they were unsure.