RESEARCH TRIANGLE PARK, N.C. (AP) — Democratic Sen. Kay Hagan and Republican rival Thom Tillis debated everything from the spread of the Ebola virus to the Supreme Court's decision to decline considering gay marriage cases during their second head-to-head encounter Tuesday night. President Barack Obama's decision to expand military activity against the Islamic State also received a fair share of attention.

Some of the most-discussed topics during the debate at the University of North Carolina Television studios, moderated by George Stephanopoulos of ABC News:

ISLAMIC STATE

On questions about what to do about the militant group In Syria and Iraq, Hagan argued that she's been clear and decisive about how to go about destroying the fighters while Tillis is "spineless on what he would do to take ISIS out." Tillis disagreed and said Hagan enabled Obama to develop a foreign policy that helped breed the terror group by removing U.S. troops from Iraq too quickly. "They left and created a vacuum in Iraq and the ISIS terrorists filled it," he said.

Hagan said she wouldn't support putting additional U.S. troops on the ground in the region because the military has been in too many wars and the country has too many domestic needs. Tillis said the president "should have everything on the table" but didn't say if he'd support additional service members overseas.

GAY MARRIAGE

Tillis, the state House speaker, defended the plan by him and Senate leader Phil Berger to intervene in federal lawsuits challenging North Carolina's constitutional amendment that banned gay marriage and was approved by voters in 2012.

The U.S. Supreme Court this week declined to take up a case striking down Virginia's law by the 4th U.S. Circuit Court of Appeals, which has jurisdiction over North Carolina. Attorney General Roy Cooper has dropped opposition to challenge North Carolina's law.

"I feel it's my responsibility, after 60 percent of the people voted that into law, to defend the laws of the state," Tillis said.

Tillis was House speaker when the General Assembly agreed in 2011 to put the constitutional amendment limiting marriage to a man and a woman on the statewide ballot. Hagan reiterated her support for gay marriage: "I do not think anyone, including the government, should tell somebody who they love or who they can marry."

EBOLA THREAT

Tillis said preventing people from African countries where the Ebola outbreak is worst from traveling to the U.S. right now makes sense to give federal health officials time to more effectively respond to the virus's threat at home. "We need to protect the safety and the security of the American people," he said. Hagan said the travel restrictions are one of several steps the government should consider but also accused Tillis of using scare tactics with his response.

MORE FIGURES

Tillis mentioned 10 times in the hourlong debate that Hagan voted with Obama 96 percent of the time — a key element of his argument that Hagan has been a rubber stamp for Democratic policies. He also took advantage of Obama's public comments suggesting that his policies are on the ballot in November in congressional races nationwide. He spent much of his time criticizing Hagan's support for Obama's signature health care law. While Hagan listed issues where she differed with Obama, Tillis didn't respond directly to a question posed to him asking that he name one issue where he disagreed from Republican leaders in Washington.

Hagan said "100 percent of the time Speaker Tillis' policies have hurt North Carolina" and repeated that Tillis helped cut public education spending by $500 million. Tillis said that's not true and lawmakers have actually raised public education spending.

WHAT'S NEXT

Libertarian Sean Haugh will participate with Hagan and Tillis in his first and likely only general election debate Thursday night at the WECT-TV studios in Wilmington. It's scheduled to be the last televised joint appearance by the candidates.