ALBANY  The fate of same-sex marriage collided with the often-dysfunctional political process here on Tuesday as the State Senate delayed a vote on a bill that would make it legal for gay and lesbian couples to marry in New York.

After an entire day of deliberations, Senate leaders emerged from the governor’s office late Tuesday with only a vague agreement that the bill would come to a vote before the end of the year.

Gov. David A. Paterson had placed the bill on the agenda for an emergency session that convened Tuesday, and gay rights advocates had been aggressively lobbying for an immediate vote. But the legislation’s prospects have grown cloudier in recent days. Supporters have had difficulty securing the 32 votes they need for approval in the Senate, and a dispute between Mr. Paterson and legislative leaders over how to close a budget deficit that now exceeds $3 billion has held up votes on major legislation.

Mr. Paterson said he would continue negotiating with legislative leaders on budget cuts this week and would call lawmakers back to Albany on Monday and Tuesday of next week. He said he would again include marriage on the agenda, but it remained unclear whether the Senate would debate it next week or wait until later in the year.