Those who see Mrs. Clinton as being at risk in Iowa say she is still far better positioned to win the nomination than Mr. Sanders, who lags by double digits in Iowa polling. Mr. Sanders is an untested national candidate who has far less money than she does, and his self-announced “democratic socialist” leanings are anathema to many Americans. Mrs. Clinton’s advisers, meanwhile, have deep experience pulling off upsets and comeback political victories, and Mrs. Clinton often performs best when she is under pressure from rivals.

But a loss in an early state like Iowa would signal a vulnerability for Mrs. Clinton at a time when she has sought to unite the Democratic Party behind her candidacy, and especially to demonstrate to its restless liberal wing that she can represent their interests. A Sanders victory could also further energize his fund-raising base.

“Certainly she could lose Iowa,” said Joe Trippi, a veteran Democratic strategist who managed Howard Dean’s 2004 campaign. If that happened, Mr. Trippi said, “mostly they’d just have to ride out the punditry and people with their hair on fire” and go on to capture the nomination.

Mr. Sanders’s rising fortunes pose a bind for the Clinton team. Directly challenging the senator on his policies and record could elevate his candidacy, alienate some liberal Democrats and make Mrs. Clinton look anxious. Yet continuing the current strategy — vigorously courting voters while hoping they conclude that Mr. Sanders is unelectable — requires Mrs. Clinton to put faith in an Iowa electorate that snubbed her seven years ago, choosing Mr. Obama and Mr. Edwards over her.