Biden in particular is banking on South Carolina, where he has enjoyed strong support among African-American voters.
He served as vice president for eight years under Barack Obama, the first black U.S. president.
Support for Biden, who once led in national polls among Democrats, has tumbled since his poor performance in Iowa.
He had said he might suffer another weak finish in New Hampshire.
"We need to hear from Nevada and South Carolina and Super Tuesday states and beyond," Biden told supporters in Columbia, South Carolina.