Voters have twice endorsed the current two-term limit for city elected officials. Bloomberg's second term is up next year.
The council will not vote on the issue Tuesday. The earliest the full 51-member body could consider the bills is Oct. 23, because each proposal would have to go through hearings and a committee first.
But all sides were already jockeying for support at City Hall on Monday at a closed-door meeting of the council's Democratic majority. Afterward, members described the discussion as charged and heated.
"There's no consensus," said Councilman Peter Vallone Jr. "There's an intense debate going on."
In addition to the two measures expected to be introduced Tuesday, two more lawmakers who also oppose the mayor's proposed path to changing the law have floated another bill that would establish a commission to consider the issue, and then put proposed modifications on the ballot in a special election next year.
As Bloomberg neared his final year in office, he struggled with what he wanted to do next. After deciding earlier this year that an independent White House bid wn believes a temporary law would be vulnerable to legal challenges. Lauder was said to be caught by surprise.
According to aides for both, Lauder and Bloomberg spoke Friday, and the mayor proposed a deal - that Lauder support his attempt to change the law permanently in exchange for a post on a commission that would study the issue and put it to voters in 2010.
Lauder is still deciding what to do, his spokesman Howard Rubenstein said Monday.
Later, Lauder issued a short statement that said, "The term limits debate is growing more difficult and divisive by the day." He said he had nothing more to add until he can speak with the mayor in person when Bloomberg returns from his overseas trip later this week.
Speaking to reporters while traveling in London Monday, Bloomberg said he did not necessarily disagree with the notion that voters should determine any term limit changes, but he said going through the council is necessary to get it done quickly.
"I think you can make a good case that he (Lauder) is right, this should be decided by the public, although at the moment, we just don't have the luxury," he said. "This financial crisis is here, and there's no ways to have a special election that would not be tied up in court for a long time."
After approving the two-term limit in 1993, voters three years later defeated a proposal to extend it to three terms. Bloomberg vetoed a 2002 City Council bill that sought to extend terms for some lawmakers.
