Vice President Joseph R. Biden Jr. paid a House call to Senate Democrats’ weekly policy lunch Thursday, pushing the president’s gun control agenda and calling the implementation of stricter gun laws a political “no brainer.”

Words come easier to Biden in a mob of reporters, however, than they do to Senate Democratic leaders when they craft legislative text.

Democrats have taken their first steps toward legislation by holding Senate Judiciary Committee hearings, but the timeline for an actual bill, whatever that might look like, is unclear. Senate Majority Leader Harry Reid, D-Nev., has said he would like any gun violence bill to move through the committee in regular order, something that would happen perhaps at the same time the panel considers a massive immigration overhaul.

Biden, who was tasked by President Barack Obama to craft the administration’s gun policy, visited his old stomping ground to remind his colleagues that gun control is a top priority of Obama’s, even if the caucus hasn’t come forward with a clear strategy to proceed and handfuls of members are reluctant to touch gun control at all.

“The visual image of those 20 little children being riddled with bullets has not only traumatized the nation but … it’s like the straw that broke the camel’s back,” Biden told reporters after meeting with Democrats in the Mansfield Room, right off the Senate floor. “I made the case for not only assault weapons but for the entire set of recommendations the president laid out.”

Of course, the assault weapons ban, introduced in the Senate by Democrat Dianne Feinstein of California, likely will be the toughest piece of any gun control package to get approved, if it gets a vote at all.

The Senate Judiciary Committee on Wednesday had its first hearing on the gun control issue and though there were some emotional moments — former Rep. Gabrielle Giffords, D-Ariz., gave brief and unexpected comments just more than two years after being shot in the head — Democrats only hinted at how they might proceed legislatively.

Sen. Richard J. Durbin, D-Ill., was one of the most aggressive questioners of the session, going after the National Rifle Association’s Wayne LaPierre in the most contentious exchange of the four-hour hearing. But by Thursday, Durbin was more subdued, conceding that there might be room for a bipartisan deal on background checks and mental health but not much more.

“I think there’s also strength in dealing with mental-health records. I think that that is an emerging bipartisan belief. I’d say next in line would be these clips and cartridges and drums as to whether there should be some limitation there,” Durbin said Thursday afternoon before lunch. “I support the assault weapon ban. I think right now, it is probably the toughest part of this conversation.”

Durbin, along with the No. 3 Senate Democrat, Charles E. Schumer of New York, spoke at the news conference last week where Feinstein introduced her assault weapon ban.

But both men are also actively engaged in the negotiations on immigration, and it’s unclear who might take the lead in the Democrats’ leadership team in wrangling votes for any package. At the moment, Reid is leaving the responsibility for the bill to Vermont Sen. Patrick J. Leahy’s Judiciary Committee. At a news conference before his caucus’s meeting with Biden, Reid said he believed the Judiciary Committee could do both bills through regular order — a tall task given that the biggest bills have rarely gone through committees in recent years, with 2010’s Wall Street overhaul legislation being a notable exception.

Some Democratic sources outside leadership have expressed skepticism that leadership has the will to do a serious gun control package. Reid himself has received contributions from the NRA and voted against 1994’s assault weapons ban, drafted in part by then-Sen. Biden. But if any one member of the administration can push senators to act, it seems Biden is the person to do it. If his comments leaving the meeting Thursday are any indication, he might be the most committed person in Washington to forcing an uneasy Democratic Conference to coalesce around reform.

“There are things that we can do — demonstrably can do — that have virtually zero impact on your Second Amendment right to own a weapon for both self-defense and recreation, that can save some lives. And the point I was making in there, and I make everywhere, this is not a difficult equation,” Biden said. “If I can prove that there is no constitutional impact on your right to bear arms and the action I’m suggesting can, in fact, demonstrably show some people could be saved, it would seem to me a no-brainer.”