Supporters of the referendum say that kind of language is alarmist and ignores a Massachusetts charter culture that prizes careful, deliberate expansion — and that would continue to do so even if the referendum passes.

“These wild assumptions that we’re going to have a charter school on every street corner, I think, are a bit delusional,” said Dominic Slowey, a spokesman for the Massachusetts Charter Public School Association. “It’s a tactic that’s meant to scare a lot of voters into thinking that the floodgates are going to open.”

Charter schools operate independently of local school committees and have a freer hand with budgets, curriculum, and hiring than traditional public schools. There were 32,646 students on charter waitlists statewide as of March, the most recent official count.

Expanding promising initiatives is one of the thorniest challenges in social policy. A successful class-size-reduction experiment in Tennessee proved difficult to replicate in California. And policymakers have struggled to duplicate effective preschool programs.

But a recent study from researchers at Columbia University, the University of California, Berkeley, and MIT shows that Boston charter schools that opened new campuses after the last round of charter expansion in 2010 were able to maintain their strong results.

The typical student at these expansion campuses, which serve large numbers of minority students, learned enough to eliminate the achievement gap between Massachusetts’ black and white students in two to three years, the authors said in a recent interview.

Christopher Walters, a UC Berkeley economist and coauthor of the study, said the results were all the more remarkable because the new campuses taught students who were poorer and entered school with lower test scores, on average, than students at other charters and traditional public schools.

But he emphasized that he was not making a judgment on whether the sort of expansion made possible by the ballot question would be as successful. “If you try to expand the charter sector to 50 or 60 percent of all [public school] students [in Boston], maybe that’s the point at which you run into trouble finding enough effective teachers,” he said. “We can’t say.”

Jon Clark, co-director of the Edward Brooke network of four charter schools, said he does not worry much about attracting talented staff to a desirable city like Boston. And he said the charter sector here has no ambition to take over public education, anyway.

That’s in part, he said, because local charter leaders are averse to the sort of “big bureaucracy” that could come with a too-large expansion of Edward Brooke or other charter networks. “One of the most powerful things to come out of the charter movement is the understanding, the realization, that great schools are made at the school level, with great principals and great teachers,” Clark said. “That’s where resources need to be concentrated.”

But opponents of Question 2 say the authors of the ballot question should have pursued a more modest charter expansion if slow, measured growth was their aim. “There are a lot of ways to responsibly raise the charter cap that don’t involve effectively eliminating it,” said David Sweeney, chief financial officer for the city of Boston.

The proposed referendum emerged during a legislative fight over lifting the state’s cap on charter schools. Many observers viewed it as an aggressive proposal designed to nudge lawmakers toward an acceptable compromise.

But Marc Kenen, executive director of the Massachusetts Charter Public School Association, said he never expected the ballot measure to force concessions from his biggest foe in the legislative battle, the Massachusetts Teachers Association. It did not, and in the end, the legislative effort died — paving the way for a full-bore ballot fight.

So if the threat of a referendum was not a negotiating ploy on Beacon Hill, then why craft a ballot measure that allows for 12 new or expanded charters when the state typically approves four or five per year?

Kenen said the number “felt like enough to give the [state] board of education the flexibility” to approve new charters as it sees fit, “while not being so much as to overload the charter school sector or any particular school district.”

But Sweeney, Walsh’s finance chief, said Question 2 could do just that. If the referendum passes, he said, the state board of elementary and secondary education could theoretically approve 12 charter schools per year in Boston, alone, and “nearly eliminate the Boston Public Schools” in the process.

In a recent analysis he prepared on the potential fiscal impact of the referendum in Boston, Sweeney wrote that if the state approved three new charter schools per year in the city over the next decade — a “conservative” estimate, by his reckoning — the share of Boston’s budget consumed by charters would surge from 5 to 20 percent, possibly forcing cuts in city services.

Charter proponents quarrel with that assumption. Historically, something closer to one new Boston charter has opened per year. And the city, they add, must be responsible for getting its own fiscal house in order. As students and money leave the traditional public schools for charters, they say, the city has to do the hard work of closing schools with large numbers of empty seats.

Samuel Tyler, president of the Boston Municipal Research Bureau, a fiscal watchdog, agreed that the city must take on some difficult reforms.

But he said Boston officials were right to raise concerns about the potential impact of Question 2. If it passes, he said, the state board of education may have to revise its approach to granting charters — paying more attention to the financial impact on cities like Boston.

The board, he said, will have to be careful “not to put [Massachusetts’] major city . . . in a financial bind.”

The most important existing cap on charter growth limits how much money charter schools can divert from individual school districts. In most districts, it’s 9 percent of “net school spending,” which includes many, but not all spending categories. In the lowest-performing districts, it’s 18 percent.

Cities like Boston that are bumping up against the cap would not be able to add many charter seats in the short run if Question 2 fails. But over time, as Boston’s school budget naturally grows, there would be more money available to ship to charters — opening up an estimated 4,000 charter seats between 2018 and 2028, according to a city analysis.

David Scharfenberg can be reached at david.scharfenberg
@globe.com.