A bipartisan group of Senate negotiators signaled Tuesday night that it has reached a deal in principle on expanding background checks to include more gun sales, in what was widely seen as the major sticking point on the biggest gun control legislation to reach the floor since 1994.

Sens. Joe Manchin III, D-W.Va., and Patrick J. Toomey, R-Pa., said they would hold a news conference at 11 a.m. Wednesday to discuss the details of the tentative deal, which was reached with the support of Sen. Charles E. Schumer, D-N.Y., and could entice a significant number of other lawmakers to sign on. Schumer told reporters that some details still needed to be worked out but that “we’re closer than we’ve ever been.”

“Tomorrow we hope to finalize it,” Manchin said Tuesday night. A Toomey spokesman added, “Sens. Toomey and Manchin continue to work on final details, but they appear close to a deal.”

The plan is expected to stop short of language currently in the bill that would require background checks on nearly all gun sales, including between private parties. Instead, Toomey aides said, the proposal would require background checks for private sales at gun shows and on the Internet, two areas that are currently exempt.

Nevertheless, support for the plan by Toomey, a reliable conservative with a top rating from the National Rifle Association, would be a major victory for Senate Democrats and President Barack Obama, who have stepped up their calls in recent days to ensure that criminals and the mentally ill do not have easy access to guns.