After Nikki Haley’s disappointing finishes in Iowa and New Hampshire earlier this year, she promised she would storm back in the next big Republican primary to deliver “a great day in South Carolina,” the state where she was born and raised and where she occupied the governor’s mansion for six years.

But her struggles to gain traction ahead of the South Carolina primary on Saturday stem in part from a simple demographic fact: The state that she left in 2017 to become Donald J. Trump’s first ambassador to the United Nations is not the one she is now running in for the Republican presidential nomination.

South Carolina has, since 2017, had a net gain of 372,000 new residents who are old enough to vote. That means that nearly 10 percent of the current electorate did not experience Ms. Haley’s state leadership. South Carolina beat out Florida and Texas last year to be the fastest-growing state in the country.

And the largest contingent of new South Carolinians hails from New York and New Jersey, many of them bringing with them an affection for the Republican front-runner, former President Donald J. Trump.

It’s all Joe Harvey said he hears when he listens to his customers at Ruby’s New York Style Bagels, which he opened 17 months ago in the Charleston suburb of Mount Pleasant after he had moved from Madison, Conn.