While declining to take a position on a proposed 4 percent income surtax on household income above $1 million, Gov. Charlie Baker in a televised interview Sunday reiterated his general opposition to new taxes and said Beacon Hill leaders should try to solve immediate budget difficulties without seeking more revenue from taxpayers who, he said, are managing their own affairs in the face of low personal income growth rates.

The so-called millionaire’s tax could surface on Wednesday, June 14, for a legislative vote that would ensure a statewide vote on it in November 2018.

Tax hike proponents, especially those interested in investments in education and transportation, have been envisioning ways to spend the estimated $1.6 billion to $2.2 billion the surtax could generate and the possibility that it could boost sluggish tax collections and offset stubborn budget deficits.

Opponents of the measure say it could discourage high earners from living in Massachusetts and warn that passage of the constitutional amendment could lead to a graduated income tax structure in which over time more people will be grouped in different tax brackets and taxed at different rates.

“There are a lot of people that have spent that millionaire’s tax six ways to Sunday already and it hasn’t even made it to the ballot yet,” Baker told WCVB’s Ed Harding and Janet Wu. “I think what we ought to do is focus on what we need to do to balance out fiscal ’17, which ends in about a month, and put a balanced budget in place for fiscal ’18, and not go back to the taxpayers thinking that they should be the source of all our solutions.”

Baker and legislative leaders are due to hear Monday about May tax revenue collections, which will influence the depth of changes that will be required to restrict spending growth and bring it in line with revenues. State officials say the fiscal 2017 revenue gap may range from $375 million to $575 million.