As Democrats across Massachusetts —including a contingent of Harvard students—turned out Saturday to pick delegates to their party’s late-May state convention, latecomer gubernatorial candidate Robert Reich won unexpectedly strong support in Cambridge.

More than 50,000 party faithful turned out across the state for the caucuses, which marked the first step in picking the Democrats’ candidate for governor.

Early polling shows the crowded democratic gubernatorial race led by state Senate President Thomas F. Birmingham ’72, a Cambridge resident.

State Treasurer Shannon O’Brien follows close behind, but both have to compete for convention delegates with Reich, former Democratic National Committee Chair Steve Grossman and former state Representative Warren E. Tolman.

Each candidate must have the support of 15 percent of the nearly 750 delegates at the state convention in order to even appear on the ballot in next fall’s Democratic primary.

Delegates may declare their support for a particular candidate but are not bound by this promise. Any attempt to tally delegate support for a particular candidate can only be determined by the guesswork of local Democratic committees and campaigns.

Based on unofficial results of this Saturday’s caucuses Birmingham and O’Brien are almost assured spots on the ballot, while Grossman is a likely third candidate, said Debra Kozikowski, vice-chair of the Massachusetts Democratic Party.

But according to state Democratic leaders, Reich still faces an uphill battle.

“I’m the vice chair of the state democratic party and I’ve never met him,” Kozikowski said.

Reich’s standing throughout the state was overshadowed by the top candidates, but Cambridge’s caucuses tipped their support behind Clinton’s former labor secretary.

In Cambridge, Reich won all five delegates in his home ward—Ward 8, which includes many Harvard Houses.

Helped by a strong student showing in Cambridge, Reich swept 19 of the 20 delegates up for grabs in the three wards that include Harvard undergraduate housing.

“There was an excellent student turnout,” said Helen Glickman, Ward 8 vice-chair, who said that hotly-contested races attracted students to the process.

“I’ve been on the ward committee since 1988 and this is the largest student turnout,” she said.

When Reich kicked off his gubernatorial bid last month—long after O’Brien and Birmingham had been on the campaign trail—he attributed his decision to run in part to a Harvard course he had lectured in last fall.