Mrs. Clinton’s advisers, struck by the strength of Senator Bernie Sanders in those two states, have been assuring worried supporters that victories and superdelegate support in Southern states will help make her the inevitable nominee faster than many Democrats expect. They point to her popularity with black and Hispanic voters, as well as her policy stances and the relationships that she and her husband, former President Bill Clinton, have cultivated. Mrs. Clinton was similarly confident at this point eight years ago, before Barack Obama and his superior organizers began piling up delegates, including in many Southern states.

In interviews, advisers said the campaign was increasingly devoting staff members and money to win the South Carolina primary on Feb. 27 while laying the groundwork to sweep Alabama, Arkansas, Georgia, Oklahoma, Tennessee, Texas and Virginia on March 1. Those Super Tuesday states are highlighted in red on maps in the offices of Mrs. Clinton’s senior aides in Brooklyn.

The eight primaries will deliver several hundred delegates for Mrs. Clinton, advisers believe, toward the goal of more than 2,200 needed to clinch the Democratic nomination. The campaign is barraging superdelegates in the South with requests for support — sometimes even jumping the gun by sending pledge forms prematurely — in hopes of adding scores of these party leaders who can bring their votes to the Clinton column at the Democratic National Convention.