"If there are unintended consequences that we see in the future, we can tweak the law to make it work best for New Jersey, as opposed to a constitutional amendment that is very difficult to do anything to once it becomes a constitutional amendment," said Moriarty.
Both proposals permit local governments to "bank" any part of the 2.5 percent increase that is not being used in a current budget year for use in any of the next three budgets.
Moriarty wants to amend a 2007 law that imposes a 4 percent cap on the local tax levy and has a sunset provision of 2012. The assemblyman said it has been effective, noting that property-tax increases have fallen from about 7 percent before it took effect to 3.3 percent last year.
The governor has said the current system has not worked because it has too many exceptions permitting towns and school districts to exceed the cap.
Christie's spokesman, Michael Drewniak, said Moriarty's plan "does not go far enough, and a constitutional cap is needed to bring real spending discipline and lower property taxes."
DiCicco, the first Republican in more than a decade to win election to an office in a Democratic stronghold, agreed.
"Without a constitutional amendment, it's kind of more of the same old look-good-, feel-good-type reforms that haven't worked for 25 years," said DiCicco.
Such an amendment would be "very clear, very hard," and would guard against exceptions - which are numerous in the current tax-levy cap - from "swallowing up the whole rule," DiCicco said.
He is sponsoring the resolution with Declan O'Scanlon (R., Monmouth), along with a second that seeks a constitutional amendment to impose a 2.5 percent cap on state spending. Senate Republicans have also introduced resolutions.
But they haven't moved in either house of the Democratic-controlled legislature, whose priority is to approve a budget by the constitutional deadline of June 30. DiCicco and other lawmakers have scheduled a Statehouse news conference for Thursday to address how the Assembly Republicans will move the governor's proposal forward.
The Republican governor wants the legislature to act by July 6, in time to put it on the ballot for November. Drewniak said that the administration had not received word on when the legislature would vote, but that "there are a lot of discussions under way."
The governor has held a half-dozen town hall meetings, all so far in Central and North Jersey, to drum up support for "Cap 2.5," modeled after an initiative enacted in Massachusetts in the 1980s. Towns can exceed the cap with voter approval.
The cap is the centerpiece of a 33-point plan Christie unveiled last month to help local governments tackle property taxes.
Moriarty, who grew up in Massachusetts, said residents may be paying less in taxes, but pay for numerous other services individually, such as trash pickup. He said wealthier towns could vote to override the cap and get superior services, while working-class communities would do without.
"We really have to think about a public-policy shift this extreme," he said, "and look down the pipeline and make sure that we have flexibility."
Contact staff writer Maya Rao
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