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Mr. Booker’s message, meanwhile, has been muddled at times by the attention that was given to his sexuality and to the private messages he sent via Twitter to a stripper in Oregon. He also has been accused of exaggerating stories for political gain and to bolster his status as a quasi-celebrity.

But with his lead dipping in the polls, Mr. Booker has refocused his attention on Mr. Lonegan, rolling out his first negative campaign ad, and casting the Republican as a tea party extremist who is out of sync with most New Jersey voters. “My opponent is going to make everything wrong with Washington even worse,” Mr. Booker said in their first debate over the weekend.

The Bloomberg ad, meanwhile, paints Mr. Booker as a post-partisan figure and highlights his role in the Bloomberg-led Mayors Against Illegal Guns, which has called for tighter gun control laws.

Booker has taken on the NRA and will fight for background checks and to get illegal guns off our streets,” the narrator in the ad says.

Mr. Lonegan rebounded from losses in two gubernatorial primary races to capture the GOP Senate nomination.

A stalwart supporter of tea party causes and former head of the New Jersey chapter of Americans for Prosperity, Mr. Lonegan has tried to link Mr. Booker to Mr. Obama and said Mr. Booker is a radical who backs liberal policies that will hurt New Jersey.

The Republican also has tried to exploit Newark’s liberal immigration policies, after the city this summer became the first in the state to opt out of the federal Secure Communities program designed to promote local law enforcement cooperation against illegal immigrants. Newark Police Director Samuel DeMaio signed a directive in July saying city police no longer would comply with federal immigration enforcement requests to hold suspects accused of lesser crimes such as shoplifting or vandalism.

The Booker campaign defended the change, telling the Newark Star-Ledger it would improve relations between the police and the city’s large immigrant community and focus local law enforcement efforts on “the real bad guys.”

But Mr. Lonegan told the paper that Mr. Booker was engaged in “political grandstanding” and said the mayor was implying, “You can come to this country illegally, you can shoplift, you can vandalize, but it’s all right.”

Mr. Lonegan wants to repeal Obamacare, dismantle the Internal Revenue Service and eliminate the Department of Education.

Mr. Christie, Texas Gov. Rick Perry, Sen. Rand Paul of Kentucky and former Alaska Gov. Sarah Palin have endorsed Mr. Lonegan.

Mr. Redlawsk said Mr. Lonegan’s best — and likely only — chance of pulling off an upset hinges on the unpredictable nature of turnout in special elections.

“If there is ever a time that someone who is out of sync with the majority can win, it is in the environment of a special election,” he said.