Foreign policy: Given her hawkish reputation, Mrs. Clinton and her top advisers have been especially alert to any signs that a left-of-center Democrat would emerge to challenge her on foreign policy.

For all the concerns about Senator Elizabeth Warren of Massachusetts and her economic populism, the person some of Mrs. Clinton’s allies kept their closest eye on regarding foreign policy last year was Senator Christopher S. Murphy of Connecticut, a Democrat who has been critical of interventionist policy in the Middle East.

Mr. Murphy is not running for president. But there is clearly an opening to run to Mrs. Clinton’s left on foreign policy.

“She’s to the right of where the party is on a lot of these issues,” one of the strategists said. Mrs. Clinton has traditionally favored a more muscular response in places like Syria, the source of one of her biggest policy disagreements with President Obama while she was secretary of state.