Monday's mass shooting at Washington's Navy Yard has revived the gun control debate in the halls of Congress, but don't expect a vote on legislation, Senate Majority Leader Harry Reid, D-Nev., said Tuesday.

"We're going to move this up as quickly as we can, but we've got to have the votes first," Reid told reporters after a closed-door lunch with the Democratic caucus. "We don't have the votes. I hope we get them, but we don't have them now."

Reid made the remarks after Sen. Dianne Feinstein, D-Calif., who authored a bill to ban assault weapons and increase background checks for gun buyers, said that the Navy Yard shooting could have been prevented if at least the background check component had become law.

Congress has for the most part shelved gun-control legislation after failing to pass a watered-down version of the Feinstein legislation earlier this year. The legislation was introduced after the deadly Dec. 14 mass shooting at Sandy Hook Elementary School in Newtown, Conn.

It faltered after most Republicans and four Democrats voted against it, with most saying they opposed the scope of the background checks.

That issue remains unresolved, said Sen. Chris Murphy, D-Conn., a supporter of expanded background checks.

"We don't know whether we have the additional five or six votes needed to bring this vote back up," Murphy said. "But at some point, people in this country are going to say enough is enough. I thought that moment was Dec. 14. God forbid we have to go through a bunch more days like yesterday."

Aaron Alexis, the accused Navy Yard shooter, was being treated for mental illness and had been hearing voices.

"This should focus our attention on people who show mental instability," Sen. John McCain, R-Ariz., said, "and whether they should have access to weapons or not. I think all Americans are in agreement on that, but how do you identify that person?"

McCain was one of three Republicans who voted for the Senate's background check legislation, which failed in a 54-46 vote in April.

He said he'd consider the bill again if it came up for another vote.

"Harry Reid sets the agenda," McCain said. "He'll decide whether we debate it or not."