The mayor used his State of the City speech Monday to defend the $205 million project.
Meeker has proposed paying for the center with a penny increase on the property tax.
The mayor is proposing a half-a-cent property tax increase in 2011 and a half-a-cent property tax increase in 2012.
When it was first pitched, city leaders were proposing a three cent increase.
The rest will be paid for by deferring other expenses, namely the sanitation and street maintenance facilities that were supposed to be built this year.
There are three new locations the city has bought and planned to develop into new worksites, one of them will be cheap and easy. The other two will be put on hold to defer costs for the Lightner Center.
The mayor expects council members to vote on the issue Tuesday.