Sen. Bernie Sanders is the favorite to be the Democratic presidential nominee in 2020, according to a poll.

Zogby Analytics surveyed 834 likely voters and found that 28 percent of respondents likely to vote Democratic said they would pick Sanders in a hypothetical Democratic primary.

The Vermont senator led former Vice President Joe Biden, who got 17 percent. Sen. Elizabeth Warren (12 percent) was the only other name to get double-digit support.

Close to one in four respondents stated that they did not know who they would vote for. The Zogby report did not specify when the poll was taken.

Sanders held a lead among most sub-groups, although Biden came out on top among voters older than 50.

Among female voters, Sanders defeated Warren by a ratio of three to one and defeated Biden two to one. The challenger to Hillary Clinton in 2016 secured 42 percent support among young voters.

The poll was released the same day as Sanders presented a new version of a bill that would give all Americans access to government-run health insurance. It calls for a strengthened Medicare to replace private insurers and for government to regulate health care costs.

"The American people are catching on to where the Republicans are coming from, they see the limitations of the Affordable Care Act and they're looking at the alternatives," Sanders told HuffPost. "And this is a rational alternative."

Though Sanders had no support in the Senate when he introduced a previous version of the plan in 2013, 16 Democrats are co-sponsoring the 2017 measure. Many of the co-sponsors are considered potential presidential candidates for 2020, including Cory Booker, Kirsten Gillibrand, Kamala Harris and Warren.

Reports suggest that Sanders' aides had expected only half as many Democrats would back the proposal.

While Republicans hold a majority in the Senate, making passage of Sanders' bill unlikely, he remains optimistic.

"You're seeing it in polling, you're seeing it in town meetings, you're seeing the American people waking up and demanding that we end this dysfunctional system and we join the rest of the industrialized world," he said.

Sanders' bill includes a four-year transition period, during which the expanded Medicare would cover people aged 55 and over. Others would be able to purchase a public health insurance plan during this period.

However, the bill does not outline how the system would be funded. Sanders presented plans for new taxes to fund an expansion of Medicare during the 2016 election campaign, but those taxes are not part of the latest bill.