New Hampshire usually winnows the field. This year may be different.

Many Democrats were hoping that New Hampshire’s famously independent voters would provide clarity when they cast their ballots on Tuesday. But with recent polls here showing Mr. Sanders and Mr. Buttigieg ahead of the field and their three leading rivals jostling for third place with a still-undecided electorate, the top candidates each began to make plans for two more diverse states, Nevada and South Carolina, as well as next month’s Super Tuesday, believing their rivals to be fatally flawed.

Mr. Sanders is planning on visiting Super Tuesday states this week. Former Vice President Joseph R. Biden Jr. dispatched one of his most prominent black supporters to host a “launch party” in South Carolina on Tuesday night, an effort to deflect attention from his anticipated struggles in heavily white New Hampshire. And Senator Amy Klobuchar of Minnesota scrambled to send staff and get television ads up in Nevada, which is next on the primary calendar…

For Mr. Buttigieg and Ms. Klobuchar, Nevada looms even larger than Super Tuesday.

Up to this point, the two Midwestern moderates have benefited from an early primary calendar focusing on small, relatively homogeneous states, and neither has yet built the kind of racially diverse national following that it will very likely take to prevail in the March primaries.

Barring a stunning upset in New Hampshire, the two campaigns view Nevada as a crucial opportunity to expand their appeal before the primary map grows to a massive scale.