While he may be unlikely to get his chance in the coming months to alter the state's tax code, Senate President Stanley Rosenberg on Tuesday said Senate Democratic leaders are "ever at the ready" to consider ways to generate new revenue to prop up areas of government spending, including public higher education.

As the House debates a budget that proposes a 1 percent increase in spending on public higher education, Rosenberg in a radio interview said the funding level proposed for the University of Massachusetts and other state universities and community colleges comes up short.

"That doesn't even cover the collective bargaining agreements that are in law," Rosenberg said during an interview on WGBH's Boston Public Radio show.

The Amherst Democrat, who represents the UMass system's flagship campus, did not say whether the Senate budget would go higher on funding for the state's colleges, but did identify what he considers to be the root cause of the budget situation.

"This is a revenue problem," Rosenberg told hosts Jim Braude and Margery Eagan.

Rosenberg predicted that on May 18 when House and Senate lawmakers consider a proposed constitutional amendment to tax high-income households a higher rate on earnings over $1 million that it will receive the necessary 50 votes to advance to the next legislative session.

The amendment, which would apply an additional 4 percent tax on income above $1 million, has been projected by the Department of Revenue to be able to generate an additional $1.9 billion in annual revenue to the state.

But with the so-called "millionaire's tax" not able to go on the ballot until November 2018, Rosenberg said the Senate remains open to other ways of generating additional tax revenue, including applying the hotel tax to Airbnb and other online room rentals.

"We have some really good ideas and we look for opportunity, but as you know we can't initiate tax bills in the Senate. We are ever at the ready with some really good ideas to make the tax system fairer," he said.

House Speaker Robert DeLeo and Gov. Charlie Baker have declared tax increases off the table this year, essentially hamstringing Senate lawmakers who would like to consider updates to the tax system that could help fund priority areas of the state budget.

House Ways and Means Chairman Brian Dempsey on Monday defended his recommended budget for higher education, which mirrored what has been proposed by Baker.

"We support the 1 percent increase but I think it important to point out we've done a lot the last couple of years," he said.

Dempsey said that since fiscal 2013 state support for the University of Massachusetts has increased 29 percent, 31 percent on community college campuses and 22 percent for other state universities.

Upon the release of the House budget two weeks ago, UMass President Marty Meehan said: "We appreciate the $508 million funding proposal put forward by the House Ways and Means Committee. UMass educates 73,000 students across the Commonwealth and is vital to our social and economic future. The support we receive from the state allows us to keep educational excellence and the dream of a better future within reach."

Officials with the state universities, however, said the House budget left a collective $30 million hole in their budgets for contractual salary increases that are not being supported by state funding.

With the salaries of public higher officials coming under increasing scrutiny, Rosenberg said it was "fair game" to look at administrative salaries and consider whether they are competitive or too high.