Students in the middle of presenting policy briefs in “Studies in Grand Strategy” Monday did not expect to see U.S. Senator John McCain walk through the door.

While campaigning in Connecticut for U.S. Senate candidate Linda McMahon, Senator John McCain stopped by Yale Monday afternoon to see the campus and participate in a policy briefing simulation for the “Grand Strategy” class taught by professors John Lewis Gaddis, Charles Hill and Paul Kennedy. Students in “Grand Strategy,” a two-semester long, application-only course for 40 students about past, present and future global power dynamics, said McCain was willing to engage in debate with them about current events and challenge their arguments, both in class and during the dinner that followed at the Union League Cafe.

“We had some significant disagreements — very lively [conversation] — but that’s what this environment’s supposed to be all about,” McCain told the News in a Monday interview.

Though he knew for about ten days that McCain might visit, Gaddis said he wanted the Senator’s visit to be a surprise because he aims to train his students never to be “rattled.”

“When you do [policy briefs] in the real world, you never know who might drop in,” he said in an email, adding that the students who presented in front of McCain “handled that very well.”

Tantum Collins ’13, who gave a policy brief on the Arab Spring during Monday’s class, said presenting in front of McCain was “a healthy mix of exhilarating and terrifying.”

Students said McCain remained engaged at the dinner as well, and would not eat until he answered all questions asked by the attendees. In addition, U.S. Senator Richard Blumenthal LAW ’73 stopped by the dinner to “welcome him to New Haven and to Yale,” Harrison Monsky ’13 said.

Before coming to Yale on Monday, McCain was in Danbury, Conn. and Norwalk, Conn. encouraging voters to support Republican McMahon in the hotly contested Connecticut Senate race against Democrat Chris Murphy.

“I’m very impressed by her,” McCain said, adding that he thinks McMahon “understands the free enterprise system” and has shown support for veterans and members of the armed services.

McCain told the News he thinks the Republican party has a “50/50” chance of gaining the upper hand in the Senate this year. He also said he believes the presidential race is “still close enough” for Republican presidential candidate Mitt Romney to win.

“Some people don’t make up their mind until they go into the ballot booth, so a lot of these elections, especially in the battleground states, will depend on voter turnout,” he said.

McCain said he believes Americans should prioritize the nation’s debt, which has increased under President Obama, as well as the role the U.S. will play overseas when considering issues at play in November’s presidential election. He added that the 2012 presidential election has been the “most negative campaign that I have ever seen, on both sides.”

“There’s a lot of wounds that may take some time to heal as a result of this,” he said, adding that Republicans and Democrats must work together better in the future to effectively pass new legislation.

Students in “Grand Strategy” said there have been a number of “high-profile” visitors — such as General Stanley McChrystal and New York Times Book Review Editor Sam Tanenhaus — since the course began last spring.

“Grand Strategy is a class on leadership, and it’s great for the students to get to meet leaders in various professional capacities,” Gaddis said.

Grand Strategy meets Mondays from 3:30 p.m. to 5:20 p.m.