BOSTON — Could taxes be on the menu when the Massachusetts Legislature begins a new two-year session in January?

As state revenues have fallen below estimates – making additional budget cuts possible – tax proposals that have been off the table in recent years may enter the conversation next year as lawmakers look for a more permanent fix to the state’s fiscal woes.

Democratic House Speaker Robert DeLeo, in a recent interview with WBZ-TV, said he would listen to opinions from economists about the possible need for new revenues, though he also made note of his disdain for broad-based tax hikes.

Senate President Stan Rosenberg and other top Senate Democrats have been more open to the idea of new taxes, but DeLeo’s refusal to consider them during the state’s annual budget negotiations made the question essentially moot. Under the state’s constitution, tax bills must originate in the House.

DeLeo’s willingness to hear the views of economists is a long way from an endorsement, and the last thing most legislators facing an election opponent in November want to talk about right now is taxes. But it could be a signal that even Democrats who consider themselves fiscal conservatives are wondering whether the state can simply manage its way out of chronic budget shortfalls.

Republican Gov. Charlie Baker would almost certainly veto any tax increase that might reach his desk. His administration has tried, with varying degrees of success, to push reforms that reduce spending in areas including the state’s $15 billion Medicaid program.

Democrats are virtually assured of keeping supermajorities in both chambers in the next session, so a Baker veto could be easily overridden if such a scenario plays out.

The next couple of weeks will provide further insight into the state’s fiscal condition. The Revenue Department will report next week on tax collections and whether they hit benchmarks established before the start of the July 1 fiscal year. Revenues came in $36 million below benchmark in July and August, continuing what state Revenue Commissioner Michael Heffernan called “adverse trends” in recent months.

Baker must then notify lawmakers by Oct. 15 if the administration intends to revise downward the current $26.2 billion fiscal year tax revenue estimate. That estimate was already downgraded by more than $600 million back in June, prior to passage of the current state budget.

The Massachusetts Taxpayers Foundation, a nonpartisan fiscal watchdog group, has recommended that revenue estimates be adjusted downward even if September collections are close to being on target.

The state’s jobless rate is at a 15-year low, and an estimated 61,000 jobs have been created in Massachusetts since the start of the year, leaving some economists and state officials struggling to explain the apparent contradiction between a growing economy and slumping tax revenues.