Over the next week, Mrs. Clinton and her aides will look for the best way to explain to viewers why she is a better choice than her nearest rival without sounding condescending to Mr. Sanders, or dismissive of his views, so she does not risk alienating his growing army of supporters.

“I’ve seen every attack people have thrown at him, and none of them have worked,” cautioned Howard Dean, the former governor of Vermont, who supports Mrs. Clinton…

Attacking Mr. Sanders’s character or lampooning his self-description as a democratic socialist, Mr. Dean suggested, will only “make him stronger, especially with his base — and we need his base.”

Mrs. Clinton is unlikely to belittle Mr. Sanders. But her debate preparations have touched on, among other things, how Mr. Sanders would accomplish some of his ambitious proposals if he was elected president, according to three people briefed on the private discussions. (Mr. Sanders’s spending proposals — free public college tuition, a $1 trillion infrastructure program and a single-payer health care system — would be financed with a variety of tax increases; both would be nonstarters under a Republican-controlled Congress.)