COLUMBIA, S.C. — As Senator Kamala Harris attempts her own version of former President Barack Obama’s historic rise from first-term senator to the White House, one of her political tests will be trying to secure the overwhelming support from black voters that buoyed Mr. Obama in 2008. Ms. Harris wants that support, but it does not come automatically.

In many ways, she is well positioned: Ms. Harris is the most high-profile and politically connected black woman ever to run for president, and she can also draw on her powerful alumni networks from Howard University, one of the most prominent historically black colleges, and Alpha Kappa Alpha, the oldest black sorority.

Yet interviews with more than 30 black voters and political leaders in early primary states like South Carolina and her home state, California, show that Ms. Harris faces challenges. She will have to persuade black activists skeptical of her record as a prosecutor; overcome sexism and a bias on the part of some voters that a female candidate cannot beat President Trump; and work to gain broader support from black men, who generally expressed more wariness about Ms. Harris in interviews than black women.

She would also need to win over left-leaning young black voters, some of whom were ultimately disenchanted by Mr. Obama’s presidency and may value political ideology more than racial solidarity.