The audience hold up placards against the Olympic Games coming to Boston, during the first public forum regarding the city's 2024 Olympic bid. (Charles Krupa/ASSOCIATED PRESS)

Boston’s fledgling bid for the 2024 Summer Olympics was thrown into chaos this week when bid organizers reversed field and declared support for a voter referendum on hosting the Games, and some are now questioning whether the group will see the bid process through to the 2017 finish line when the International Olympic Committee selects the host city.

With poll numbers showing that only about a third of Bostonians support hosting the Olympics, the group behind the Boston 2024 bid announced Tuesday it would seek an up-or-down vote on the Games, most likely on the November 2016 ballot, and would drop its bid if voters statewide — or even within Boston itself — said no thanks.

“We are definitely in the early stages of our outreach to the community,” Doug Rubin, a member of the Boston 2024 executive bid committee, said in a telephone interview Wednesday. “We’ve got over 20 meetings scheduled around the state to talk with voters and work with them on strengthening the bid. . . . As we go through the process, we all feel really good that the people will get behind this.”

Still, the move to support a referendum is a high-risk gamble on the part of bid organizers that public sentiment, which has plummeted in recent months, will shift significantly in favor of the Games in the next year and a half. Should they lose that gamble and fail to submit a bid to the IOC, it would represent an unthinkable embarrassment for the U.S. Olympic Committee, which selected Boston as the U.S. bid city in January over competing bids from Washington, Los Angeles and San Francisco.

“If Boston drops out, it would [signal] the USOC didn’t do their homework” in selecting the bid city, said Andrew Zimbalist, Smith College economics professor and author of “Circus Maximus: The Economic Gamble Behind Hosting the Olympics and World Cup.” Zimbalist said Boston 2024’s support of a referendum is a “prudent position to take” given the waning public support. “But they are now painted into a corner by taking that position.”

The IOC is scheduled to select the 2024 host city in September 2017 from a group of bidders that is expected to include Rome, Paris and Hamburg, Germany, among other cities.

“It’s very early at this stage. We’re very confident Boston can deliver a great bid and a great Olympics,” USOC spokesman Patrick Sandusky said Wednesday. “If [a referendum] is how [the Boston bid leaders] feel is the best way to demonstrate that the people of Massachusetts and the citizens of Boston are behind [the bid], we fully support them doing it.”

The leaders behind Washington’s failed bid for the 2024 Olympics declined to comment Wednesday on the struggles of their Boston counterparts. One person connected to the DC 2024 bid, when asked whether there was “no chance” of the bid process being reopened, replied, “I wouldn’t say ‘no chance,’ but it’s highly, highly unlikely.”

Still, last month, the Boston 2024 group quietly purchased a $1 million insurance policy that would indemnify the group in the event it pulls out of the bidding and triggers a $25 million penalty payable to the USOC, as first reported by the Wall Street Journal.

Rubin said Wednesday that was done at the insistence of Boston Mayor Martin J. Walsh (D) “to protect the city because we made it clear early on we were going to do everything we could to protect the city. I can assure you Boston is committed to this.”

If the Boston referendum fails in 2016, it would be too late for the USOC to shift its bid to another city since countries vying to host the Games must submit official, binding bid letters, including the name of their host city, in September.

When Boston first received the USOC’s nod as the U.S. bid city, a slight majority of Bostonians supported the bid, according to a poll conducted by radio station WBUR . But what followed was a series of public missteps by the bid group and city officials, including the revelation that city employees were barred from making negative comments about the Games and another that former Massachusetts governor Deval Patrick (D) was reportedly being paid $7,500 per day to lobby on behalf of Boston 2024.

In the aftermath of those revelations, the ban on negative comments was lifted, and Patrick announced he would work for the group for free. But in a new WBUR poll in February, public support for the Games fell to 44 percent.

“It’s much more important that those numbers be high 2 1/2 years from now than it is that they be high now,” Scott Blackmun, CEO of the USOC, said in a conference call with reporters after the release of the February poll numbers. “So we have plenty of time to allow this trajectory to unfold and complete confidence in Boston 2024’s ability to do that.”

Then came the near-disastrous snowfalls of February, which broke records for Boston and the outlying areas and shut down the region’s ancient “T” subway system. As the city finally dug out from all the snow, apparently a sizable number of its residents decided the public transportation system could never handle an Olympics. WBUR’s March poll showed support for the Games was down to 36 percent.

“You can’t underestimate the drag that the breakdown in public transportation had in the month of February,” said Mike Barnicle, a former Boston newspaper columnist and current contributor to MSNBC. “The winter was so fierce, and the T was virtually shut down for five weeks in what is the Olympic capital of cynicism: Boston. That had a lot of people thinking about cost and how much the taxpayers would have to bear.”

Although the Boston 2024 group has vowed that no public funds would be used to stage the Olympics, 65 percent of Bostonians believe public funding will be needed, according to the latest WBUR poll.

“I don’t know a single person who believes that — that they’re going to build a soccer stadium and all these other facilities at no cost to the taxpayer?” Barnicle said. “No one believes that.”