What do free bus rides, new taxes on the wealthy and a stiff drink in a movie theater have in common? All three have the support of lawmakers in the New York State Legislature.

These ideas and thousands of others were tucked into the Senate and Assembly budget proposals released this week, offering a glimpse of legislators’ positions as Albany’s annual budget battle royale kicks off. Gov. Kathy Hochul must come to a consensus with leaders in the State Senate and Assembly on how to spend more than $230 billion by the state’s April 1 budget deadline.

The fact that all three leaders are Democrats does not mean there is any less to haggle over: Taxing the rich, tenant protections and school funding are all up for debate once more as Ms. Hochul, a centrist from Buffalo, will be forced to find common ground with an increasingly left-leaning Legislature.

And while those debates have sometimes become intractable — last year’s budget was a full month late, after Ms. Hochul insisted on tightening the state’s bail laws — Democrats in both houses are eager to avoid a prolonged ordeal with a consequential general election on the horizon.

In January, Ms. Hochul unveiled her $233 billion spending plan, which called for significant investments in mental health care, public safety and artificial intelligence research, as well as $2.4 billion to address the migrant crisis in New York City. But she also proposed cuts to education funding and health care that have drawn criticism.

In their proposals, Democrats in the Senate and Assembly pushed back against Ms. Hochul’s desired changes to education funding while offering their own proposals on how to solve the state’s housing crisis, make transportation more effective and accessible, and more.