Campaigning with Texas Gov. Rick Perry, Lonegan accused the Obama administration of being unwilling to compromise.
Lonegan, a former mayor of Bogota, Bergen County, played down the impact of the partial shutdown, which has halted services deemed nonessential.
"I'm really sorry it's inconvenient that our national parks are closed," he said.
About 800,000 federal workers were to be furloughed as a result of the shutdown. The campaign of Newark Mayor Cory Booker, the Democratic nominee, said 31,000 federal workers in New Jersey were affected.
Addisu Demissie, Booker's campaign manager, said Lonegan had "trivialized" the shutdown's effects, "showing just how callous, extreme, and out of touch with regular people he is."
The back-and-forth came as a new poll showed a tighter race than many had expected. Lonegan trails Booker by 13 points, according to a Monmouth University poll released Tuesday. The special election is Oct. 16.
In an interview, Lonegan added that he would not vote to raise the debt ceiling without significant spending cuts. He dismissed the possibility of a default as a "mythological concept." The fight over raising the nation's statutory borrowing limit is expected to bring another fiscal clash in Washington this month.
As part of a bill to fund the government, House Republicans on Monday proposed delaying by one year implementation of the individual mandate - one of the central pieces of the health care law - that requires every American to buy health insurance or pay a tax.
Senate Democrats swiftly rejected that offer, saying such unrelated proposals should be considered separately from a spending bill needed to keep the government operating.
Online exchanges where people can buy health insurance under the Affordable Care Act, called by some Obamacare, opened Tuesday.
Perry, who campaigned Tuesday with Lonegan in anti-Obamacare rallies across New Jersey, was less enthusiastic about the shutdown.
"Nobody's happy about it," he said. "I guess they got their point over; they're both all big boys and girls. Nobody blinked. Now government's shut down. OK. Now, get back to work."
He criticized Obama as "refusing to negotiate."
"The president will negotiate with the president of Iran. He will negotiate with other people," Perry said. "So why not sit down with the House and the Senate and find a solution so we go forward when Americans are really concerned about this health care bill?"
Perry, who ran in last year's Republican presidential primaries, followed U.S. Sen. Rand Paul (R., Ky.), who is considered a possible contender for the party's 2016 presidential nomination, as another high-profile politician to stump for Lonegan.
Lonegan said he invited Perry because he admired his stewardship of Texas' economy.
While Garden State voters may not be swayed by the conservative governor of Texas, Lonegan still stands to gain from Perry's endorsement, said Ben Dworkin, director of the Rebovich Institute for New Jersey Politics at Rider University.
"If you're Lonegan and you bring in Rick Perry, you can mobilize your base, raise money from your base, and get yourself in the paper again, which he's been doing with such regularity that he's closed the gap from 30 points to 15 points between him and Cory Booker," Dworkin said.
The Lonegan campaign said Tuesday it had raised more than $1 million in the last two months, three times as much as it had raised until then.
Earlier Tuesday, U.S. Rep. Robert E. Andrews (D., N.J.) and U.S. Rep. Debbie Wasserman Shultz (D., Fla.), the chair of the Democratic National Committee, tied Lonegan and Perry to tea-party Republicans whom they blamed for the government shutdown.
Andrews said Lonegan would find more people who agree with him in rural Texas than he and Perry would find in New Jersey.
"These guys are in the wrong zip code," Andrews said on a media call arranged by the Booker campaign.
The Booker campaign used news of the shutdown to attack Lonegan with a television ad Tuesday that will run on cable networks in New York and Philadelphia and on broadcast and cable in Atlantic City.
The ad notes that Lonegan supports the shutdown and paints him as "too extreme for New Jersey."