John Kerry's campaign is trying to lower expectations ahead of the next round of presidential contests.
Primaries or caucuses are being held in seven states on Tuesday, and recent polls suggest Kerry could win at least five of them. But his staff is playing down talk of a sweep.
Aides say the Massachusetts senator would be happy with a few victories and a bulk of the 269 delegates up for grabs.
Most of the attention is focused on South Carolina, where one poll shows Kerry tied with native John Edwards and and another gives Edwards the lead.
In Oklahoma, polls show Kerry, Edwards and Wesley Clark locked in a three-way race.
Most polls show Kerry with a commanding lead over the other Democratic hopefuls in Missouri, Arizona and North Dakota, and a smaller lead in New Mexico and Delaware.
Kerry won the Iowa caucuses and the New Hampshire primary.