But after his successful reelection in November, political analysts say, Sweeney is positioning himself for a gubernatorial run - touring the state talking Hurricane Sandy, for example - and could face a primary from the left, perhaps from Jersey City Mayor Steven Fulop.
Gun-rights activists say Sweeney has broken a promise not to bring gun-control bills to the floor and have soured on the senator they once considered an ally. (The National Rifle Association has donated about $10,000 to Sweeney's campaigns since 2003, according to data compiled by the National Institute on Money in State Politics.)
After Sweeney supported other gun-regulation measures last year, the Association of New Jersey Rifle and Pistol Clubs - the NRA's state affiliate - downgraded his record on guns from A to D.
"For many years, the Senate president was supportive of the Second Amendment and gun rights, and for a time had a well-deserved A," said Scott Bach, the group's executive director. "That changed in 2013."
And the magazine restriction, Bach said, "is a third-rail issue for gun owners, hunters, and sportsmen."
In an e-mail, a spokesman for Sweeney said he had "always supported the Second Amendment and has had a good working relationship with advocates of like mind. That being said, he has never shied away from taking on the gun lobby on issues of gun-violence prevention."
The spokesman, Chris Donnelly, noted that Sweeney introduced background-check legislation last year and "wasn't going to let" attacks from gun-rights groups "stop him from fighting for these commonsense measures."
Sweeney has said he changed his position on the magazine-restriction legislation after meeting with parents of children slain in December 2012 at Sandy Hook Elementary School in Newtown, Conn.
On Thursday, dozens of gun-rights supporters turned out for an Assembly hearing in Trenton, decrying a bill they said would encroach on their Second Amendment right to bear arms and punish law-abiding citizens without deterring criminals.
Opponents also said they feared the bill would ban scores of guns they already own. The bill's primary sponsor, Assembly Majority Leader Louis D. Greenwald (D., Camden), testified that wasn't the case and argued that restricting magazine capacity would force mass shooters to reload more frequently, increasing the chances that potential targets could escape or attack the assailant.
An Assembly panel on Thursday advanced the bill, which now heads to the full Assembly and also must be considered by the Senate.
The question is whether gun-rights groups have the clout in New Jersey to effectively lobby legislators to vote against the proposal or, if it becomes law, to remove them from office.
Some gun-rights activists point to Colorado, where the NRA backed successful recall elections last year of two state senators who helped pass a package of stringent gun-control bills through that Democratic-controlled legislature.
The NRA spent $397,000 on the recall elections, Colorado state records show. Opponents of the recall, led by gun-control crusader and former New York City Mayor Michael Bloomberg, spent about $3 million, according to news reports.
Of perhaps greater utility to the NRA than money are its 4 million or so members, which the organization can mobilize with a simple e-mail alert. The NRA declined to comment for this article.
"I don't think the shock wave from Colorado, whatever it might have been, really affects states like New Jersey and New York, simply because there's greater support for gun regulation in those states anyway," said Robert Spitzer, a political scientist at the State University of New York at Cortland and author of The Politics of Gun Control.
New Jersey's Democratic-controlled Legislature passed a dozen gun-violence bills last year. Christie vetoed three others. A September 2013 Rutgers-Eagleton poll showed a majority of Garden State residents supported the gun-control bills Christie rejected; for example, 64 percent said they favored a ban on .50-caliber rifles.
New York also passed a comprehensive gun-control package last year, including a seven-round magazine limit. Gun-rights groups protested those measures, "but their real impact so far has been zero, aside from supporting lawsuits against the new law," Spitzer said.
A federal judge struck down the magazine law, though New York already had a 10-round restriction.
In New Jersey, even some leading gun-rights activists acknowledge they are unlikely to stop the magazine bill from passing now that it has Sweeney's support.
"We need to show up in force. And we need to just keep in mind that our remarks and testimony are really being directed toward Gov. Chris Christie," Frank J. Fiamingo, president of the New Jersey Second Amendment Society, said in an interview before Thursday's hearing.
Christie, a possible contender for the GOP presidential nomination in 2016, may not need much lobbying. By vetoing the magazine-capacity bill, he could "reassure the Republican base that he's still a conservative, even though most attention is focused on the George Washington Bridge," Spitzer said, referring to an alleged political payback scheme.
In December, Christie's administration declined to defend a challenge to the state law requiring a special permit to carry a handgun, prompting a rebuke from an appeals court judge.
At a town-hall meeting Thursday in Mount Laurel, Christie said he would assess the magazine-capacity bill if it gets to his desk, though he did mention his veto of the .50-caliber weapon ban.
Skip Brockner, a Collingswood NRA member who asked about the bill Thursday, said he was satisfied by Christie's answer.
The point of his question, Brockner said in an interview, was: "We're going to put a bug in your ear. . . . It's not liked."
Inquirer staff writer Maddie Hanna contributed to this article.