A bill to authorize millions of dollars in capital spending is simmering on the back burner as New York state lawmakers discuss legalizing marijuana, giving driver’s licenses to undocumented immigrants and other issues in the final week of their annual session.

It is an unusual twist for June, because spending matters usually are settled when the budget is adopted by April 1. But a $175.5 billion budget was approved this year without allocating significant new money for capital projects, which could include infrastructure upgrades or economic-development spending.

Now, Gov. Andrew Cuomo is holding back the introduction of the capital-spending bill, hoping to entice legislators to negotiate on a series of issues.

The Democratic governor has presented measures he is hoping legislators will pass alongside the spending bill, including the legalization of gestational surrogacy to help infertile or LGBT couples form families, and changes to sexual-harassment standards.

On Wednesday, Mr. Cuomo said he and lawmakers are trying to work out their differences on climate-change legislation.

Some legislators criticized the governor for using the spending bill as a bargaining tool. “Disturbingly, these are the kinds of things that happen in trade-off deals very close to the end” of the session, said state Sen. Liz Krueger, a Manhattan Democrat.

On Tuesday, Mr. Cuomo said he wasn’t focused on the details of the spending bill, noting that he and legislators have their own funding priorities. The governor is seeking money to reconstruct flood-damaged areas along the St. Lawrence River and Lake Ontario, and to upgrade mass transit in Buffalo.

Ms. Krueger said she would like to see additional money for the New York City Housing Authority, the operator of the largest public-housing system in the U.S.

Assemblywoman Deborah Glick, another Manhattan Democrat, said facilities at the state’s public colleges could benefit from investment.

Assemblywoman Helene Weinstein, a Brooklyn Democrat and chair of the Assembly Ways and Means Committee, said her colleagues also are seeking supplemental funds for road and bridge repairs. “There’s a number of things that are outstanding,” she said.

Ms. Weinstein said she believes Mr. Cuomo’s office will take the lead on introducing a spending bill because legislators are constrained in which budgetary measures they can put forth. She said there have been general discussions about the measure, but she doesn’t know how much money would be authorized.

Critics expect a spending bill would include more funding for the State and Municipal Facilities Program (SAM), where the eligible projects are loosely defined in statute and specific projects are later earmarked by lawmakers.

E.J. McMahon, research director for the Empire Center for Public Policy, a fiscally conservative think tank, questioned the need for these projects. His organization found recent SAM allocations paid for projects he deemed frivolous such as a skate park and a local highway garage. “It’s this huge mutual back-scratching,” he said.

The Citizens Budget Commission, a nonpartisan fiscal watchdog, said the state should be wary of approving capital projects outside of the budget process.

“Absent an emergency, state spending should be allocated during the budget process, when state leaders can adequately consider priorities and trade-offs,” David Friedfel, the organization’s director of state studies, wrote in a recent blog post. “It is not justifiable to add more debt to fund pork-barrel spending.”

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