For nearly four years, Mayor Bloomberg and the City Council speaker, Gifford Miller, have shared City Hall, often agreeing to agree rather than allowing their political differences to sidetrack policy initiatives and spending plans. As Mr. Miller attempts to energize his mayoral campaign, however, budget negotiations have fallen behind schedule and council officials have begun preparing a backup plan.

The city budget is due in less than two weeks, and council officials said that the dispute over one of both men’s top priorities, a plan for disposing of the city’s trash for the next 20 years, is preoccupying officials and slowing budget negotiations.

“The SWMP negotiations are kind of at a stalemate,” the chairman of the council’s Committee on Finance, David Weprin, said, referring to the solid waste management plan. “It’s just a significant distraction as we’re going through the budget negotiations. It has delayed things.”

Mr. Weprin said the council and the mayor should be able to move ahead simultaneously with trash and the budget, which are related only by timing, but he said, “I think a lot of this is caught up in politics – politics involving individuals, who voted with whom.”

A sticking point in the trash dispute is a transfer station on the Upper East Side, where the mayor wants garbage put onto barges instead of being trucked out of state.

The 91st Street site sits in Mr. Miller’s council district.

Last week, the speaker – who leads a 48-member Democratic caucus on the 51-member council – successfully rallied a slim majority of council members to vote down the mayor’s plan.

The mayor vetoed the council’s decision, and the council is expected to vote again on the issue next week. It would need a two-thirds majority to override the veto.

Mr. Miller’s spokesman, Stephen Sigmund, said the speaker’s mayoral ambitions have nothing to do with the slow process on the budget talks. But he said the Bloomberg administration’s “unwillingness to negotiate on the garbage issue is presenting an impediment.”

On Wednesday, council leaders met to begin the process of crafting a backup budget.

“We’re going to be prepared to do our own budget if it comes to that,” Mr. Weprin said, adding that the council has prepared a backup plan in each of the past four years.

Although the deadline is approaching and the mayor’s team has yet to provide the council with what it would consider a compromise offer, he said the two sides will probably reach agreement by the end of June.

A spokesman for the mayor, Jordan Barowitz, said, “Budget talks are progressing and [we] expect to reach an agreement before the end of the month.”

He said the garbage issue and the budget are progressing on “parallel tracks.”

The executive director of a budget advocacy group attributed the lateness of the budget and the posturing surrounding the process to politics.

“The budget is always more politicized than it should be,” Bonnie Brower of City Project said. “This year it’s more politicized than it usually is.”

Ms. Brower predicted that if Mr. Miller is able to rally two-thirds of the council to override the mayor’s garbage veto, the budget situation “could get ugly.”

“If he’s able to override the mayor’s veto, I think there could be real trouble,” she predicted. “The mayor doesn’t take well to losing, and plus his plan happens to be better.”

The deputy research director at the Citizens Budget Commission, Elizabeth Lynam, said that as the end of the month nears, nerves might fray, but that it would be “quite unusual” if there were no budget agreement by July 1. It would also be unusual for the council to pass its own budget.

The last time that happened was in fiscal year 1999.

The Manhattan Institute’s budget expert, E.J. McMahon, said it’s not uncommon for non-budget issues to get in the way of budgets in Albany.

But he said: “What happens in Albany is a non-budget issue intervenes and then they do nothing. In the city, if the council does nothing, they revert to the prior year’s budget, with the mayor having a significant amount of control.”

Mr. McMahon said it’s also not uncommon for politics to intervene in the budget process.

“Politics is the nature of the beast,” he said. “I would hope the budget process has got politics in it. The question is, is politics involved in dictating the level of taxation or the level of spending?”