Aides say there probably will be three main packages of gun-control legislation over the coming months, with one anchored by the assault-weapons ban, which is considered the most difficult. Another set of proposals will include an effort to establish universal background checks for all firearm sales in retail stores, gun shows or private exchanges. The other piece would include limiting the size of gun magazine clips.

Senate Democrats have yet to decide the order: whether to start with background checks — their most likely victory — and try to build momentum, or to save that for the final piece so the effort ends on a positive note.

Reid has remained silent on the individual gun-control proposals. His prepared statement last Wednesday, after Obama announced the proposed legislation, left gun-control advocates and gun rights supporters parsing each sentence: Some focused on Reid’s hailing of the president’s “thoughtful recommendations,” while others noted his vague promise that “the Senate will consider legislation.”

Some of Reid’s fellow Democrats are worried. Feinstein said she had a private conversation with Reid to voice her displeasure after he told a Nevada television station that, given the current political environment, it might be futile to move an assault-weapons ban through Congress. “You have to try, you can’t sit back and just let the gun organizations call public policy,” Feinstein said in an interview last week.

On Tuesday, Reid sounded more open to a bold approach. “This is an issue that we’re not going to run from,” he told reporters. “It’s an issue we need to talk about. . . . It may not be everything everyone wants. But I hope it has some stuff in there that’s really important.”