Hillary Clinton’s political ascent can be traced to the time in 1999 when she expressed her support for dairy farmers in the upstate New York village of Endicott. And the summer that year when she shunned Martha’s Vineyard to vacation in Skaneateles, and promised voters in the depleted industrial city of Schenectady that as a New York senator she would revive the upstate economy.

The strategy helped Mrs. Clinton win her 2000 Senate race by double digits, a victory fueled by the unlikely support of white working-class voters in upstate New York who had previously voted Republican but were won over by the first lady’s attention to their underserved area.

Now, 16 years later, Mrs. Clinton is again promising to bring jobs back to the region as she courts the people who helped secure her first election victory. But this time her message is colliding with a surprisingly potent threat from the left and doubts about her ability to deliver.

Her current effort, which advisers say is critical not just to winning the New York primary on April 19 but to swaying voters nationwide to Mrs. Clinton’s style of pragmatic problem solving, comes as she looks to rebound after losing six of the last seven primary elections to Senator Bernie Sanders of Vermont.