Six months since the mass shooting at Sandy Hook Elementary School in Newtown, Conn., parents of some of the youngest victims plan to visit Capitol Hill again this week to meet with lawmakers about crafting a bill to impose stricter gun laws.

(Scott Olson / Getty Images)

Gun-control groups are scheduling the parents to attend another round of meetings and other public events -- including a reading of the names of people killed by guns since the Newtown shooting -- in a push to restart debate on the issue sometime in the coming months.

But try as they might, prospects for a new gun-control bill appear to be no better than in April, when the Senate swiftly defeated a bipartisan gun-control bill and delivered an embarrassing defeat to President Obama. Plus, with the Senate already scheduled to spend most of June debating a bipartisan immigration overhaul bill, there's little room for discussion of other issues.

On Monday, Vice President Biden -- normally ebullient when discussing the administration's priorities -- seemed less than certain that gun-control will return to the fore in the Senate.

"I’ve got to talk to Harry [Reid] and see what the game plan here is," Biden told reporters after swearing in Jeff Chiesa as the new senator for New Jersey. But, Biden added, "I personally haven’t given up, nor has the president."

Biden and Reid are scheduled to speak in the coming days to explore possible options, according to aides, who say that there are no imminent plans to reintroduce a gun bill in the Senate.

Public support for the bill defeated in April remains strong, with roughly nine in 10 Americans backing provisions regarding an expanded gun background check system. In a Washington Post-ABC News poll released last month, two-thirds of all Americans say the Senate did the wrong thing in blocking the proposal, with majorities of Democrats, Republicans and independents in agreement. Those who say the chamber did the wrong thing blame Republicans rather than Obama by more than 3 to 1.

Despite those numbers, no senator who voted against the gun bill has significantly shifted his or her position on the issue since April.

For example, Sen. Jeff Flake (R-Ariz.) -- who voted against the bill and admitted that his popularity suffered because of his stance -- said in a recent interview with The Washington Post that he didn't think the Senate would debate gun-control again in the near future.

"I don’t think they’re going to come back on it. They’ve got a long way to go. And frankly, I just don’t see people who voted against it moving on their position," Flake said.

But gun-control advocates believe that the gun bill's lead sponsor, Sen. Joe Manchin III (D-W. Va.), could change the measure to make it more accommodating to Flake and other senators who voted against it, including Mark Pryor (D-Ark.) or Mark Begich (D-Alaska). Possible revisions include changing the definition of commercial gun sales that would require a background check, or carving out exceptions for far-flung rural communities located hundreds of miles from the nearest gun store.

"We're willing to make lots of changes," said Mark Glaze, executive director of Mayors Against Illegal Guns (MAIG), the group backed by New York Mayor Michael I. Bloomberg (I). But, Glaze said, none of the revisions could go so far as to erode the general spirit of the legislation, which is to expand background checks to most commercial sales and stiffen penalties for people who buy firearms for people ineligible to own them.

Glaze said his group and others remain hopeful that Manchin can work out a deal, calling him "the most determined and charming" advocate for those seeking changes in federal gun laws.

"Everyone knows what we need: We need a couple of Republicans and a couple of Democrats to come together to help make something happen," Glaze said.

With prospects for new legislation still months away, gun-control groups are also turning their attention to another political battle: The years-long fight to confirm a new permanent director to lead the Bureau of Alcohol, Tobacco and Firearms, a position that has been vacant since the role first required Senate confirmation in 2006.

A Senate Judiciary subcommittee is scheduled to hold a confirmation hearing Tuesday for the agency's acting director, B. Todd Jones, who has been on the job on an interim basis for more than 18 months. Obama nominated Jones to take the job permanently in January, just weeks after the Newtown shooting.

Dan Gross, president of the Brady Campaign to Prevent Gun Violence, said Monday that the lack of permanent leadership at the ATF "has gone on far too long, depriving the bureau of the stable leadership and the focus to carry out its vital missions including preventing violent crime."

David Chipman, a former ATF special agent who now advises MAIG on gun policy, noted that the lack of permanent leadership at ATF means the agency "cannot effectively lead a national effort to prevent gun violence." The ATF's budget and staffing has stagnated since 2005, the last full year ATF was led by a confirmed director, dropping from 4,878 people to 4,770 employees by fiscal 2012, he said.

But here again, gun-control groups face a daunting battle. Republican lawmakers, the National Rifle Association and other gun rights groups have successfully stopped the Senate from confirming a new ATF director since President George W. Bush’s first nominee, Michael J. Sullivan, was blocked by three Republican senators who accused Sullivan of not doing enough to end the agency's “overly burdensome regulatory policies” on gun owners.

Later, the NRA fought Obama’s first nominee, Andrew Traver, who headed the ATF’s Chicago field office but was accused of being “deeply aligned with gun-control advocates and anti-gun activities.”

This time, Jones faces criticism from Sen. Charles E. Grassley (R-Iowa) and others about a housing discrimination case in Minnesota and about an ATF operation in Milwaukee he oversaw. Jones is also facing questions for decisions he made in the aftermath of the bungled Phoenix gun operation known as "Fast and Furious."

Bottom line: The raw politics of the gun debate haven't changed, and any new push this week by the victims of gun violence -- however emotional it may be -- is more likely to just remind Americans that Congress hasn't addressed the issue rather than actually compel lawmakers to act.

Follow Ed O'Keefe on Twitter: @edatpost