By Joan Gralla

(Reuters) - New York state looked on track to easily beat its April 1 deadline for passing its budget the second time in a row, but political analysts say that after several hurdles were cleared last week, optimism appears to have withered.

The negotiations might come closer to the deadline due to new pressure on legislators from unions angry about Democratic support for new legislation cutting pension benefits as well as from lawmakers upset about new lines redrawing election districts.

Governor Andrew Cuomo, a Democrat, has proposed a $132.5 billion budget to close a deficit of $2 billion.

When asked on Tuesday about getting his plan done this week, he told TALK 1300 AM radio show: "I just want to get it done by April 1."

Last year's budget was the first on-time accord in five years.

Monday's decision by New York's biggest public employees union, the CSEA, to cut donations and support for lawmakers who backed cuts in pension benefits could slow negotiations. This puts more pressure on legislators - all of whom stand for re-election in November - to try to offer unions other budget sweeteners.

Carl Korn, a spokesman for New York State United Teachers, which represents teachers around the state, said: "There are still opportunities for the legislature to cast the 'right' votes."

His union and others seek more aid for education and health care and want the state's securities law, the Martin Act, expanded so that public pension funds can recoup recent investment losses that resulted from fraud.

Public unions have a number of items on their wish list, including avoiding budget cuts by raising the corporate alternative minimum tax to 3.5 percent from 1.5 percent, said Ron Deutsch, executive director of New Yorkers for Fiscal Fairness, an advocacy group that backs these initiatives.

Business groups and wealthy individuals say they already have done enough to raise revenue, citing last year's enactment of a payroll tax to help fund the Metropolitan Transportation Authority and a personal income-tax hike for the well-to-do.

Democrats typically rely on unions for donations and get-out-the-vote programs. Their support, then, is crucial to Cuomo's hopes to keeping the Assembly's big Democratic majority and overturning the Senate's GOP leadership, which has only a two-vote margin, political analysts said.

A spokesman for Assembly Speaker Sheldon Silver, a Democrat, had no immediate comment.

A spokesman for Senate Majority Leader Dean Skelos, a Republican, said the state Senate wants an ontime budget.

(Reporting by Joan Gralla; Editing by Jan Paschal)