ALBANY — A plan to raise taxes on millionaires across the state could take center stage in the battle for control of the state Senate, with supporters of the tax hike promising to mount a campaign to pressure the Republican-led Senate into backing the scheme.

The campaign would target regions of the state in which residents have been hit hard by soaring property tax bills, such as Long Island and upstate in Erie County, and reach New Yorkers through door hangings, mailers, the Internet, and possible radio and television advertisements.

Daniel Cantor, the executive director of a labor-backed political organization, the Working Families Party, said his group is determined to make sure the public is aware that the Republican-led Senate, led by Majority Leader Dean Skelos, is blocking the proposal.

The Republicans are holding on to a slim majority in the 62-member Senate, which would flip to the Democrats if the Republican Party loses two of its seats in November.

“We are pretty optimistic that when voters and citizens understand that Skelos and company are stonewalling in favor of millionaires over the middle class that there will be valuable repercussions,” Mr. Cantor said. He said his group has shown “the capacity to inject an issue into an electoral situation and make it come alive.”

The tax increase on people who earn more than $1 million a year was approved in the Assembly this week as a way to raise $2.6 billion to help pay for a property tax relief plan set up to reduce tax bills for households earning less than $250,000.

Those in favor of the millionaire’s tax and the property tax plan it would fund noted that 19 Republican Assembly members voted in favor of the plan, which they took as a sign that the Senate would eventually cave on the issue.

The tax increase is opposed by Governor Paterson and Mayor Bloomberg. Critics have said it would drive wealthy New Yorkers from the state and inflict further harm to the economy. Mr. Skelos is supporting a cap on property taxes that would prevent bills from rising by more than 4% each year, which the Senate approved earlier this month.

Lawmakers were in Albany for a special legislative session on Tuesday that ended yesterday morning after the Senate voted to approve more than $1 billion in cuts to the state budget over two years. The Assembly stayed at the Capitol late into the night on Tuesday, taking its vote on the proposal just after 2 a.m.

The reductions include $127 million in cuts to health care and Medicaid spending this year and another $374 million next year; $102 million in cuts to the City University of New York over two years, and $257 million in local assistance payments to local governments and nonprofit organizations over two years. The cuts will reduce the state’s budget deficit to $5.4 billion from $6.4 billion.

Mr. Paterson appeared with the majority and minority leaders of the Legislature yesterday morning to hail the cuts. He has been warning New Yorkers that the fiscal health of the state is in danger and called lawmakers back to Albany to figure out a way to start closing the budget gap.

“The winds of change have come to Albany,” he said yesterday. “We have never cut this amount off the budget without taxing in anyone’s memory. We have never gone into the budget and made these kinds of cuts in an election year and we have never gone into the budget in August.”