George Bush, on a campaign swing through Illinois, predicted Saturday his "liberal" Democratic rival would divide the nation while Michael Dukakis told a rally in South Dakota he would win the White House "by a nose."

Speaking to an estimated 10,000 supporters in Sioux Falls, S.D., Dukakis intensified his populist "we're on your side" campaign pitch and pounded away at Republican elitism."Remember the old saying, `the rich get richer?' " Dukakis asked. "Well, Mr. Bush wants to make that the law.

"They (Republicans) want to help people who live high off the hog. We want to help the people in this country who raise the hogs," Dukakis said. "They want to help the people on easy street. We want to help the people on Main Street. We're on your side. We're on the side of farm families in this country."

Bush, leading a nine-bus convoy through the Republican strongholds of suburban Chicago, predicted the American public would not be fooled by Democratic charges of elitism.

The Dukakis campaign believes the populist theme has helped it rebound in the polls in recent days and hopes it will lead Democrats to an incredible come-from-behind victory over Bush a week from Tuesday.

An upbeat, forceful Dukakis told the crowd, which included supporters from Iowa, Minnesota, Kansas, North Dakota and Nebraska, that he expects to win.

"We're moving," Dukakis said. "You can taste it, feel it, sense it, can't you?

"This is going to go down to the wire and it's going to be won by a nose, and if this one is won by a nose I don't have to tell you who's going to win," said Dukakis, making fun of his prominent nose. "You're looking at the next president of the United States."

But three new polls showed Bush ahead, and the vice president picked up three more more newspaper endorsements - The San Antonio Light, The Seattle Post-Intelligencer and The Denver Post. But none of the editorials lavished praise on the vice president, and all expressed disappointment with the 1988 campaign.

A poll of New Jersey voters showed Bush leading in that state by 14 points. The poll, conducted for The Newark Star-Ledger, had Bush leading Dukakis 52 percent to 38 percent.

A Chicago Sun-Times-WLS-TV poll of 1,242 likely voters in Illinois showed Bush edging Dukakis 49 percent to 41 percent with 10 percent undecided. A Chicago Tribune poll of 2,344 voters in Illinois, Texas, California, Florida and New York showed Bush leading 49 percent to 40 percent with 11 percent undecided.

Illinois is one of the fiercest battlegrounds for the candidates, with 24 electoral votes at stake. The state is viewed as a swing state, with its largest city, Chicago, primarily Democratic, but its governor, James Thompson, a Republican. Thompson joined Bush for the tour.

When Bush got down to the business of campaigning, he accused the "liberal" Dukakis of dividing the nation along class lines.

"I am not going to let that liberal governor divide this nation. I am going to keep us together," he said.

Bush was asked later on the bus to explain his statement.

"It's very clear that that's what they're trying to do, saying he's for the working man and all of this," Bush said.

"Values are the thing. The working man is going to decide on, and a working woman, that I've got those values on our side. That's exactly what I mean. He's trying to go talking about my elitism, resurrecting all this in the end. The American people are not going to be fooled by it," he said.