The top Democratic presidential candidates are locked in a close race in the 2020 Iowa caucuses, with Senator Elizabeth Warren slightly ahead of Senator Bernie Sanders, Mayor Pete Buttigieg of South Bend, Ind., and former Vice President Joseph R. Biden Jr., according to a New York Times/Siena College poll of likely Democratic caucusgoers.

Ms. Warren appears to have solidified her gains in the first voting state while Mr. Buttigieg has climbed quickly to catch up with Mr. Sanders and overtake Mr. Biden, the onetime front-runner. Ms. Warren is drawing support from 22 percent of likely caucusgoers, while Mr. Sanders is at 19 percent, followed by Mr. Buttigieg at 18 percent and Mr. Biden at 17 percent.

The survey is full of alarming signs for Mr. Biden, who entered the race in April at the top of the polls in Iowa and nationally. He is still in the lead in most national polls, but his comparatively weak position in the earliest primary and caucus states now presents a serious threat to his candidacy. And Mr. Biden’s unsteadiness appears to have opened a path in the race for other Democrats closer to the political middle, particularly Mr. Buttigieg.

The poll reveals a race in flux but not in disarray, framed by a stark debate about the direction of the Democratic Party and by a degree of fluidity arising from Mr. Biden’s travails. In the early states, at least, the former vice president appears to be buckling on one side to the expansive populism of Ms. Warren and Mr. Sanders, and on the other to Mr. Buttigieg’s calls for generational change.

While no single candidate has a decisive advantage, the strongest currents in the party appear to be swirling around candidates promising in different ways to challenge the existing political and economic order.