The Working Families Party came close to the mainstream of Connecticut politics in 2011 as a newly elected Gov. Dannel P. Malloy and lopsided Democratic majorities in the legislature handed the union-backed group a signal victory: Passage of the first state law mandating paid sick days in the U.S.

Six years later, the group’s distance from the center of power in the state is reflected in the Democrats’ shrinking numbers in the General Assembly and Malloy’s admonition Monday that even talking about WFP’s latest priority — a 19.5 percent surtax on the earnings of hedge fund managers — is unspeakably bad politics.

“The mere discussion of it in our state, year after year, is disruptive to commerce and people’s thinking,” Malloy said.

Malloy’s comments came while answering questions about falling tax revenues, which he blamed in part on the volatility inherent in the state’s reliance on the richest 1 percent of taxpayers for 30 percent of its income tax revenue. The latest revenue estimates are that the state can expected nearly $600 million less in total revenue than originally projected in the next fiscal year.

The Working Families Party is pushing for a state surtax on hedge fund managers to help balance the budget and to offset a federal “carried interest” tax break that Donald J. Trump called an inequity during his campaign, but not one addressed in his administration’s recent outline of proposed tax reforms.

The provision taxes the income of hedge fund managers as capital gains under the federal code, capped at 20 percent. Ordinary income is taxed at a top rate of 39.6 percent. The proposed surtax is designed to make up the difference.

Malloy, who was cross-endorsed by the Working Families in 2010 and 2014, but is not seeking a third term in 2018, declined to define what his comments Monday say about the current state of his relationship with the group.

“I don’t have a beef with the Working Families. I don’t have a beef with anyone having an idea,” he said.

But Malloy questioned the wisdom of pressing one state to address a federal tax break, saying a surtax might yield a windfall for Connecticut, but it would be short-lived as hedge funds fled to other states.

“You might get one or two years before all moving trucks had done their work,” Malloy said, quickly adding that passage of the bill was impossible. “That’s not going to happen. My hunch is people know it’s not going to happen. So why engage in rhetoric that makes matters worse, not better?”

Lindsay Farrell, the executive director of the Working Families in Connecticut, said the organization is used to working on the fringes of politics, taking years to move issues like paid sick days and a livable minimum wage closer to the center.

“These are the things we have to fight for. We’re used to having to make a space for them that didn’t already exist in the political dialogue,” Farrell said. “My organization, we’ve never really been in the mainstream.”

But they were closer in 2011, when Malloy took office as Connecticut’s first Democratic governor in two decades, the winner of the state’s closest gubernatorial election in 56 years. His 6,404-vote margin of victory fell within the votes he won on the WFP’s ballot line.

Democrats lost 15 seats in the state House in the 2010 election, but they still began Malloy’s tenure as governor in 2011 with a 99-52 advantage. They’ve lost another 20 seats since then and now hold a 79-72 majority.

The WFP has scored electoral victories, even as it’s lost clout in the General Assembly.

It backed Josh Elliott in a Democratic primary challenge to House Speaker J. Brendan Sharkey, D-Hamden, last summer, when Sharkey ultimately chose not to seek another term. In a special election last week, Joshua M. Hall won a special election for a House seat in Hartford on the Working Families ballot line, defeating the Democratic Party-endorsed candidate.

“In many ways in American politics, it’s a populist moment,” Farrell said.

She noted Bernie Sanders strong showing last year as a populist challenger from the left and Trump’s populist appeal to the right.

Paid sick days was a fringe issue when the Working Families pushed it in 2011, but it’s now a mainstream political issue. With Malloy’s backing, Connecticut also took the lead in 2014 on the minimum wage, becoming the first state to pass a law eventually raising its minimum to $10.10, the level sought by President Obama. Other states have moved to $15.

Farrell said that Connecticut’s fiscal crisis — and independent expenditures made last year in targeted legislative races by the Connecticut Business and Industry Association — have made the state legislature’s mood more conservative.

“The budget stuff obviously has taken a toll on the Democratic caucus,” Farrell said. “Nobody likes any of the solutions — nobody likes cuts and layoffs, and there is a pushback on raising revenue. It puts the caucus in a politically difficult position.”

Joe Brennan, the president of the CBIA, said the political climate for business has improved in Connecticut, but mainly because legislators are sensitive to the state’s slow recovery from the recession of 2008.

“It’s better, but it’s better for bad reasons,” Brennan said. “A lot of the things we’ve been saying and predicting, unfortunately, have come to fruition.”

House Speaker Joe Aresimowicz, D-Berlin, whose chief of staff is married to Farrell, said members have the right to propose whatever legislation they wish, even if it has no chance of success. The bottom line on the hedge fund tax is it is not going forward.

“I understand what the governor was saying,” Aresimowicz said. “I don’t necessarily disagree, but where do you find the balance between restricting policy discussion and being opposed to it? It’s not a bill that was brought up for a vote. I think that speaks volumes to where it’s at now.”