TEANECK, N.J. — Mayor Giuliani crossed the Hudson River last night, campaigning on his muscular foreign policy and taking a fresh swipe at Senate Democrats who voted yesterday to include a timetable for withdrawing troops in an Iraq war spending bill.

“I hope that the president vetoes it, and I think the idea of giving your enemy a timetable for retreat makes no sense to me,” he said, calling the Senate vote a “terrible mistake” that hinders America’s efforts to create “an Iraq that acts as a bulwark against terrorism rather than a headquarters for terrorism.”

Mr. Giuliani made the remarks at a kosher delicatessen in this heavily Jewish pocket of New Jersey before heading to a private fundraiser nearby.

He had barely slathered mustard on his corned beef on rye sandwich when diners began peppering him with Middle East policy queries.

“I believe in Reagan’s approach of peace through strength,” he answered the diners.

Asked by one diner how he would approach President Ahmadinejad of Iran, Mr. Giuliani called the Persian Gulf nation a threat to Israel, adding that he feared Iran would give nuclear weapons to terrorists.

“I would make it clear to him that he is not going to have nuclear weapons,” he said. “That’s not an option.”

Mr. Giuliani faced questions from the press about a former police commissioner, Bernard Kerik, whom Mr. Giuliani had recommended to be federal Homeland Security secretary.

“Voters have a right to evaluate everything about me. They have a right to evaluate the mistakes that I’ve made, of which there were mistakes,” he said.

Before the event, Mr. Giuliani had to wade through heavy rush hour traffic on the George Washington Bridge. He arrived almost 45 minutes late. Still, locals hoping to meet him arrived early and stretched out their meals to be sure they were dining when he was.

“Mr. President,” Zelda Stern, who works at a yeshiva, beckoned to Mr. Giuliani as she ate with her grandchildren.

After Mr. Giuliani glad-handed and moved on to another table, Ms. Stern said she thought Mr. Giuliani had a good chance of winning his White House bid next year.

“One-hundred percent,” her 8-year-old grandson, Andrew, said.

“Well,” Ms. Stern told her grandson. “Not 100%.”