Bernie Sanders took a resounding victory in the Nevada caucuses on Saturday, bolstered significantly by Latino voters and extending his lead in the race for the Democratic presidential nomination.

Some party insiders raised concerns about whether the progressive senator from Vermont can hope to beat Donald Trump in November.

The next state to vote is South Carolina, which holds its primary next Saturday.

On Sunday, on ABC’s This Week, the most powerful Democrat in the southern state was asked if Sanders describing himself as a democratic socialist would be off-putting to voters.

“A lot of people think so,” congressman Jim Clyburn said. “I do believe it will be an extra burden for us to have to carry. This is South Carolina, and South Carolinians are pretty leery about that title ‘socialist’.

“And so I think that that would be a real burden for us in these states or congressional districts that we have to do well in. If you look at how well we did [in the 2018 midterms] and look at the congressional districts, these were not liberal or what you might call progressive districts. These were basically moderate and conservative districts that we did well in.

“And in those districts, it’s going to be tough to hold on to these jobs if you have to make the case for accepting a self-proclaimed democratic socialist.”

Sanders’ win also prompted alarm among the punditocracy. The MSNBC Host Chris Matthews landed in hot water after comparing the senator’s surge – he ran strongly in Iowa and won New Hampshire – to the Nazi invasion of France.

The former Bill Clinton strategist James Carville was more measured, saying on the same network: “If you want to vote for Bernie Sanders because you feel good about his programme, because you don’t like the banks on Wall Street, you don’t like pharmaceuticals, that’s completely legitimate, I understand that.

“If you’re voting for him because you think he’ll win the election because he’ll galvanize heretofore sleepy parts of the electorate, then politically you’re a fool – and that’s just a fact.”

The demographics of Sanders’ victory, however, suggested that he may have earned a foothold in diverse states which mirror the Democratic base more closely than Iowa and New Hampshire.

In Nevada, according to CNN entrance polls, Sanders took 51% of the Latino vote, way ahead of any rival, and did well with African Americans.

Perhaps indicating his confidence that Nevada would not be a close finish, Sanders gave his victory speech in Texas. The Lone Star state votes on 3 March, also known as Super Tuesday – the day on which the candidacy of the billionaire former New York mayor Mike Bloomberg will be tested at the polls for the first time.

“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.

No clear rival has yet emerged. In Nevada, former vice-president Joe Biden finished second, followed by former South Bend, Indiana, mayor Pete Buttigieg and Massachusetts senator Elizabeth Warren. Buttigieg was Sanders’ main rival in Iowa and New Hampshire. Biden is targeting a win in South Carolina, where he is popular with African American voters.

Speaking to CBS’s Face the Nation, Biden disputed that South Carolina was “my firewall” and said: “I’m running for the same exact reason when I started: to restore some dignity to the office, to make sure African Americans and minorities get treated well, and … to unify the country and the party.”

He also said drops in his support among African Americans in South Carolina were down to greater spending by other candidates, including the billionaire Tom Steyer.

Despite a bruising week of news reports and a poor debate performance, Bloomberg is aiming to emerge as a hugely well-financed standard-bearer for moderates who fear a Sanders nomination.

Kevin Sheekey, his campaign manager, said in a statement: “The Nevada results reinforce the reality that this fragmented field is putting Bernie Sanders on pace to amass an insurmountable delegate lead.”

Sanders supporters maintain that he can play well in racially diverse areas. Alexandra Rojas, executive director of Justice Democrats, a leftwing group born out of the senator’s 2016 campaign, said that in Nevada, “in a diverse electorate that looks the most like Super Tuesday states, Democrats chose Bernie Sanders as their candidate to defeat Donald Trump.

“It’s clear the Democratic voters with the most energy behind them look and think a lot more like [New York congresswoman Alexandria Ocasio-Cortez] than Joe Biden.”

Polls show Sanders leading in California and Texas, huge Super Tuesday prizes with large Latino populations.

Not all mainstream Democrats professed themselves worried about Sanders. On CNN’s State of the Union on Sunday the Connecticut senator Chris Murphy said his Vermont counterpart was as viable as the moderates against him.

“I think Bernie Sanders will beat Donald Trump,” he said. “I think Joe Biden would beat Donald Trump. I think Elizabeth Warren would beat Donald Trump.”

In general, polling backs that up although notional head-to-heads are tight and Trump’s approval rating is climbing. A CBS News poll released on Sunday said 65% of voters expect the president to win re-election.

Murphy continued: “What we need is a candidate who has a base of enthusiastic supporters … who’s authentic, who speaks truth to power, who can throw a punch and who can take a punch.

“I think anybody who’s polling in the top four or five fits that bill, but Bernie’s base of support, the enthusiasm behind him, I think speaks to the strength of his candidacy – both in the primary and as a general election candidate as well.”

Saying he was “not endorsing anyone”, Murphy added: “Bernie’s done very well in the opening primaries, but this thing is not a done deal.”