There’s about to be a new game in town, and it’s called Sandy relief.

Gov. Andrew M. Cuomo has raised the ante for lawmakers and administration officials who have pledged support for coastal states hard hit by the storm.

The New York Democrat’s call for $30 billion in federal aid over 10 years to help homeowners and businesses and rebuild infrastructure vital to his state’s economy adds a new and costly element to a tangle of fiscal issues already facing Congress as it reconvenes Tuesday for a post-election session.

With the amount of money needed for other states, particularly New Jersey, still to be determined, disaster relief funding becomes a potential sticking point or bargaining chip in negotiations aimed at averting the fiscal cliff of tax increases and automatic spending cuts due to arrive with the new year.

Early indications are that disaster relief will become part of the negotiations toward a catchall spending bill that would fund the government for the remainder of fiscal 2013 and perhaps replace the sequester. A stand-alone emergency supplemental spending bill could more easily become a magnet for other spending proposals.

House and Senate appropriators favor an omnibus, aides said, which would give them flexibility to shift funding between federal agencies helping the Northeast clean up after the devastating storm.

But aides said it is too early to know how much money is needed and exactly how it should be provided. “Before approving more taxpayer dollars, it’s important Congress has all the necessary information on what is needed and how the money will be spent in order to ensure the funds will be put to good use and not invite waste,” a House GOP aide said Monday.

Cuomo set a high mark for New York’s needs on Monday with his announcement that the state needs such funding for an ambitious effort to clean up after the storm and replace damaged infrastructure with transportation and utility grids that are more resilient. His office made the announcement ahead of President Barack Obama’s visit to New York City on Nov. 8.

Officials in the area say the storm caused up to $50 billion in damage. New York City has spent more than $100 million on storm relief, and Mayor Michael Bloomberg announced he will spend an additional $500 million for an emergency plan to repair schools and hospitals.

New Jersey Gov. Chris Christie has not put a cost estimate on the extensive damage to his state’s shore communities. Christie, a Republican, started a private disaster fund that already has drawn millions of dollars in contributions.

When Sandy hit, the Federal Emergency Management Agency had $7.8 billion in its Disaster Relief Fund for fiscal 2013, including some money that had not been spent in fiscal 2012. But because federal programs are running on a continuing resolution (PL 112-75) through March 27, the first half of the fiscal year, FEMA has only about $3.1 billion immediately available, agency officials have said.

Whether Congress approves additional funding through a supplemental appropriations bill or an omnibus carrying the federal accounts through next Sept. 30, efforts to use a measure as a “Christmas tree” for spending earmarks could prove difficult because the August 2011 debt limit law (PL 112-25) limits discretionary defense and domestic spending to $1.047 trillion for the year. Congress could appropriate about $5 billion more for disaster funding under a disaster relief cap in the law.

The cap limits disaster funds to $11.8 billion in this fiscal year. Congress earlier this year appropriated $6.4 billion under the disaster cap, leaving up to $5.4 billion more that could be added. If even more funds were needed, the law allows Congress to appropriate them under an emergency designation.

In a letter last week to Speaker John A. Boehner, R-Ohio, and Minority Leader Nancy Pelosi, D-Calif., 44 House members asked the leaders to support additional funding if needed.