Hillary Rodham Clinton’s campaign is grappling with a difficult question: How can she contrast herself with Bernie Sanders in next week’s Democratic presidential debate and beyond, without employing the sort of attacks that could boomerang to harm her?

For months, Mrs. Clinton has gingerly approached Mr. Sanders, the Vermont senator, who has routinely drawn tens of thousands of Democrats to his rallies and who is rivaling her in polls of Iowa and New Hampshire voters. She has seldom mentioned his name, let alone criticized him.

But while Vice President Joseph R. Biden Jr. may be a looming threat, Mr. Sanders poses more immediate concerns to Mrs. Clinton and her aides.