In the aftermath of Bernie Sanders’ victory in Nevada and as the South Carolina primary looms, the Democratic party establishment continues to grapple with the increasing likelihood that the Vermont senator, a self-proclaimed socialist, will be its nominee for president.

Sanders’ latest victory showcased his popularity among a more representative chunk of the Democratic base – Latinos, African-Americans and union members – than voted in Iowa and New Hampshire, the first two states in the primary.

“We’ve brought together a multigenerational, multiracial coalition that is not only going to win Nevada, it’s going to sweep this country,” Sanders said in San Antonio, Texas, on Sunday.

In the next eight days, 15 crucial elections will take place.

Centrists in the party having failed to coalesce around a moderate candidate, the nomination could be there for Sanders’ taking after South Carolina votes on Saturday or after Super Tuesday, 3 March, when 14 states follow suit. Only 2.5% of the delegates needed to win the nomination at the convention in July were on offer in Iowa, New Hampshire and Nevada.

He had a massive literacy program. Is that a bad thing? Even though Fidel Castro did it? Bernie Sanders

Sanders began his crucial week planning extra rallies in Super Tuesday states but also under fire for comments made in an interview with CBS News broadcast on Sunday night.

Sanders told 60 Minutes he opposed the “authoritarian nature” of Cuba under the Castro regime, but said Fidel Castro did some good things.

“He had a massive literacy program,” he said. “Is that a bad thing? Even though Fidel Castro did it?”

The Florida Democrats Donna Shalala and Debbie Mucarsel-Powell were among those to criticize Sanders’s muted praise for the deceased Cuban president.

“I’m hoping that in the future Senator Sanders will take time to speak to some of my constituents before he decides to sing the praises of a murderous tyrant like Fidel Castro,” Shalala tweeted.

“The Castro regime murdered and jailed dissidents, and caused unspeakable harm to too many South Florida families,” Mucarsel-Powell wrote. “To this day, it remains an authoritarian regime that oppresses its people, subverts the free press and stifles a free society.”

Sanders’ comments are likely to feature in Tuesday night’s Democratic debate in Charleston, South Carolina.

Former New York mayor Mike Bloomberg, who has spent more than $460m of his own money in an attempt to establish himself as the Democrat best placed to beat Donald Trump, indicated on Monday that he would also target Sanders on gun control.

The Bloomberg campaign released a video attacking the senator for his mixed record on the subject.

Before Sanders was elected to Congress in 1990, for example, he received support from the National Rifle Association because his Republican opponent had supported banning assault weapons. The Bloomberg video also highlighted Sanders’ support for a law that helps stop mass shooting victims suing gun manufacturers and the five times he voted against a bill which called for waiting periods before acquiring guns and instant background checks on gun purchases.

Sanders addressed the issue in the New Hampshire debate earlier this month.

“Until the last – two years ago – we had virtually no gun control legislation at all, and I represented that perspective,” he said. “The world has changed, and my views have changed.

“And my view is right now, we need universal background checks. We end the gun show loophole. We end the so-called strawman provision. We make certain that we end the sale and distribution of assault weapons in this country.”

We are going to let people know how we feel about these candidates James Clyburn

Bloomberg has poured money into the gun control movement but it is unclear if his cash can overcome the damage wrought by other candidates’ focus on his own record regarding women and people of color.

At the last debate, in Nevada, the former mayor failed to craft a convincing response to criticism of his controversial policing policy, stop-and-frisk, which disproportionately impacted minorities.

The favored centrist candidate in South Carolina is Joe Biden, who remains popular with African American voters, a dominant presence in Democratic contests in the state, after serving for eight years as vice-president to Barack Obama.

A CBS News poll taken before Nevada, where Biden placed second, showed him in the lead in South Carolina with 28% support. Sanders was second with 23%, followed by the second billionaire in the race, Tom Steyer, with 18%.

In 2016, Hillary Clinton dominated South Carolina, winning with 73% of the vote to 26% for Sanders.

Biden, who has denied suggestions that that his campaign will be over if he does not win South Carolina, is expected to receive a well-timed endorsement from the House majority whip, Jim Clyburn, the highest-ranking African American in Congress.

“We are going to let people know how we feel about these candidates, and it may not line up with Nevada or New Hampshire or Iowa,” Clyburn told ABC News on Sunday.

As Trump tweeted gleefully about supposed establishment attempts to block Sanders, some Democrats called on candidates including the Minnesota senator Amy Klobuchar and former South Bend, Indiana mayor Pete Buttigieg to exit the race in order to consolidate the moderate vote.

All the remaining candidates, however, have said they plan to stick around for Super Tuesday.

Buttigieg, who like Sanders declared himself the winner of the muddled Iowa caucuses, used his concession speech in Nevada to warn against a “rush” to nominate Sanders to face Trump in November.

The senator, he said, is a “disaster in waiting”.