BEACON HILL is approaching a proposal to reduce the state’s income tax with a club in one hand, an olive branch in the other, and a furrowed brow to top it all off.

Just a few weeks after the House voted to condition access to federal tax cuts on the failure of a ballot question that would reduce the state income tax rate, Speaker Ron Mariano suggested a willingness to chat with the influential business groups pushing the measure about a possible compromise.

On the same day, the Senate voted to allow the state to align with the new federal tax provisions without any mention of the ballot measure, a break from the House that revealed divisions in strategy among top Democrats. Legislative leaders have also hinted they might respond to a voter-approved income tax cut by pursuing some kind of tax increase elsewhere on the state’s ledger.

Altogether, the array of comments and actions represents something of a mixed message. Lawmakers are at once deeply skeptical of the entire ballot question process, think it’s been coopted by interest groups, and also want those same groups they slam to come to the table and chat about alternatives.

The income tax cut question could be one of the most impactful decisions in years. A report from the Center for State Policy Analysis at Tufts University estimated that, once fully implemented, the change could erase $5.1 billion in revenue from the state’s coffers while providing about $1,250 in annual relief for an average middle-class household.

For months, the Democrats who control the House and Senate as well as Gov. Maura Healey have been warning that the proposal would unleash massive pain on state government, forcing cuts to popular services and programs. But leaders of the House took their concerns a step further, moving to write an ultimatum about the ballot question’s fate into a Healey proposal dealing with federal tax code changes.

States have some authority to decide whether they will define personal and corporate taxable income the same way as the federal government. New measures in the reconciliation package Congress and President Trump approved last year will change several corporate tax provisions, and if Massachusetts automatically conformed with those updates, it could cut hundreds of millions of dollars in state revenue. So Healey suggested instead phasing them in over a few years, softening the immediate impacts while still allowing businesses to access the relief eventually, a contrast from some other states that “decoupled” from federal definitions altogether.

Last month, the House wove Healey’s proposal into a broader spending bill with one major change: a rider declaring that if the tax cut ballot question passes this fall, the state would not implement the federal corporate tax changes at all. That means voters would essentially face a choice between cutting the state income tax or gaining the relief promised by federal changes.

It’s unusual for legislation to link a statutory change to the outcome of a future statewide vote, and the idea quickly drew blowback from businesses leading the campaign. Brian Shortsleeve, one of the GOP challengers hoping to unseat Maura Healey, described Mariano and his team as “doing their best Tony Soprano impressions and trying to extort voters.”

So far, however, House Democrats have failed to secure buy-in from their counterparts across the hall. The Senate redraft of the same spending bill delays federal tax conformity the same way Healey proposed, dropping the House’s idea to use that relief as electoral leverage.

Instead, Senate budget chief Michael Rodrigues said lawmakers should “respond to whatever the voters in Massachusetts send us” — after the fact, not preemptively.

“We’re very comfortable with what the governor proposed” on tax changes, said Rodrigues, who has long argued the ballot question is a bad idea.

House and Senate negotiators will now need to agree to a final, compromise version of the bill, which seeks to carve up about $1.2 billion in extra money collected from the surtax on wealthy households and appropriate hundreds of millions of dollars to mid-year spending priorities, such as a push to hire more caseworkers at the Department of Transitional Assistance. It’s possible representatives prevail during those talks and convince senators to follow the House’s this-or-that-not-both approach to tax, and it’s also possible they decide to drop the idea altogether.

Hours before the Senate approved the legislation, Mariano struck two tones at once about the income tax cut while speaking with business leaders. At an event hosted by the Greater Boston Chamber of Commerce, Mariano contended that the House vote to link the ballot question’s fate to federal tax code changes “isn’t a message or a political tactic,” but is instead a “reflection of the fiscal reality that the Commonwealth could very well be facing by the end of the year.”

“If the question passes, we will have no choice but to make significant budget cuts to services and programs that our residents rely on,” Mariano told attendees. “That could mean cuts to school budgets, health care funding, infrastructure spending, the MBTA, support for cities and towns, and to state investments in economic development.”

“It could also force the Legislature to consider the need for new sources of revenue,” he added — or, in other words, tax hikes.

Yet alongside his dire warnings, Mariano also extended an invitation to the backers of what he deemed a “ham-fisted approach” to tax policy. The Quincy Democrat said he hopes the businesses behind the campaign are “willing to sit down with us and consider alternatives to their current approach.”

“If they believe, as we do, that the Commonwealth can tackle the issues of affordability and competitiveness in a fiscally responsible manner, the House is open and willing to work on solutions to those challenges together,” he said.

Speaking with reporters after the event, Mariano said a compromise could entail work to address “some of the problems that we have that directly affect the proponents of the question,” like the billions of dollars Massachusetts businesses will need to pay in higher unemployment insurance taxes following a Baker administration payment error.

One of the main organizers behind the ballot question took Mariano’s remarks as a “message of openness,” even with the occasional barbs laced in by the speaker.

“We have a problem with our economy, and I think everybody wants to find a way to solve that. That’s what I took [Mariano’s comments] to be: recognition that there has to be something done,” said Jim Stergios, executive director of the Pioneer Institute, a think tank that’s among the leaders of the campaign.

Lawmakers at times have brokered deals with ballot question backers in which the Legislature passes a more modest version of a bill and campaigns agree to suspend their efforts.

In 2018, for example, Beacon Hill enacted a law known as the “grand bargain” that increased the minimum wage, launched a paid family and medical leave program, started an annual sales tax holiday weekend tradition, and phased out time-and-a-half pay on Sundays and holidays. In exchange, several groups suspended campaigns for ballot questions that would have trimmed the state’s sales tax, increased the minimum wage, and launched the paid leave programs.

It’s unclear if any concrete talks are taking place, or are gaining traction, this time around. Asked if he was open to scrapping the push for an income tax cut ballot question should the Legislature act, Stergios replied, “I think you’re dealing with reasonable people.”

“Everybody has a job, and people in state government have to think about budget contingencies. I get why someone might raise some of these issues,” he said of the various gripes lawmakers have raised. “I completely get it.”

Another tool legislators have is the ability to change a ballot question after passage. Sometimes, they do so to clean up a measure’s implementation without changing its intention. Other times, they substantially alter or altogether spike voter-backed policies, like the 2003 repeal of a law providing public financing of campaigns approved at the ballot in 1998.

“We’ll cross that bridge when it comes,” Rodrigues said about the prospect of amending what voters decide this November. “I’m not going to speculate on what’s going to come before us. When something comes before us, we’ll deal with it.”

Far more apparent than the prospect of a compromise or a legislative response is the degree of frustration among top lawmakers. Even as he sought to welcome income-tax-cut supporters to discuss alternatives, Mariano took a swipe at their campaign.

“It’s just such nonsense that it’s insulting to me, as someone who follows public policy, that they think that they can solve problems that way,” he said. “I don’t know if you notice a little bit of anger in that, because I’m a little bit tired of this.”

Jordan Wolman contributed reporting.