Gun control supporters made progress in both chambers this week, as a Senate committee advanced a nominee to become the first permanent director of the Bureau of Alcohol, Tobacco, Firearms and Explosives in seven years and a House panel approved a significant funding increase to improve background checks on gun sales.

Both of those efforts, however, still have a long way to go before advocates — who have clamored for tougher gun policies since the December school shooting in Connecticut — can declare victory.

The Senate Judiciary Committee’s 10-8 party-line approval Thursday of B. Todd Jones, the ATF’s acting director and a U.S. attorney in Minnesota, left little doubt that Republicans intend to fight the nominee on the floor.

Led by Sen. Charles E. Grassley of Iowa, Judiciary Republicans point to allegations made by one of Jones’ subordinates in his U.S. attorney’s office that the nominee engaged in workplace retaliation over protected whistle-blowing. Grassley calls the allegations “alarming” and contends an investigation into Jones by the Office of Special Counsel, an independent government watchdog, should be allowed to conclude before the Senate acts on the nomination.

Moreover, Sen. John Cornyn, R-Texas, signaled that the floor fight over Jones may turn into a proxy debate over gun rights. “As a committed defender of Texans’ Second Amendment rights, I have serious concerns that Mr. Jones would infringe on these rights,” Cornyn said.

Democrats are eager to see Jones confirmed, given that the ATF has not had a permanent director since 2006, when Congress first required Senate confirmation for the position. But if the nomination turns into a broader debate over gun control, it is unclear if Democrats could beat back a Republican filibuster — or even muster enough votes within their own caucus to confirm Jones on a simple majority vote, should Majority Leader Harry Reid, D-Nev., resort to the so-called nuclear option and change the Senate’s filibuster rules.

The politics of gun control are murky in the Senate, where four red-state Democrats joined with Republicans to defeat a relatively modest, White House-backed expansion of the background check system in April. Those same senators — Max Baucus of Montana, Mark Begich of Alaska, Heidi Heitkamp of North Dakota and Mark Pryor of Arkansas — and others are likely to face pressure from the National Rifle Association, Gun Owners of America and other groups to oppose Jones.

The open investigation into Jones is unlikely to improve his standing among those senators, and may lead the Republicans who voted for the background checks proposal in April — John McCain of Arizona, Susan Collins of Maine, Mark S. Kirk of Illinois and Patrick J. Toomey of Pennsylvania — to break from Democrats and oppose him.

Meanwhile, Reid’s threatened use of the “nuclear option” has already inflamed tensions with the GOP and, if acted upon, could diminish the chances of bipartisan support for any of President Barack Obama’s nominees, particularly one for an agency that has been at the center of the political fight over gun control. Gun Owners of America has already urged its members to contact their senators and urge them to oppose Reid’s effort to “destroy the Senate rules that are blocking passage of gun control.”

Funding Boost

In the House, the prospects may be more encouraging for gun control supporters after an Appropriations subcommittee on Wednesday approved a spending bill for Commerce, Justice and science-related agencies that includes $55 million for states to improve the National Instant Criminal Background Check System, the database gun dealers use to determine whether prospective buyers are dangerous and should be turned away.

Mayors Against Illegal Guns, the gun control advocacy group co-founded by New York City Mayor Michael R. Bloomberg, praised the bipartisan funding increase and said it amounts to more money for the background check program “than has been appropriated in the previous four years combined.”

Rep. Frank R. Wolf, the Virginia Republican who chairs the subcommittee, said in a letter to his constituents Friday that the additional money for background checks — together with other funding for school safety improvements — are “tangible and significant steps toward reducing gun violence.”

Wolf said his efforts to expand funding for background checks began before recent shootings in Connecticut and Aurora, Colo., but that those attacks have “made the need for increased funding all the more important.”

Yet it is unclear how a provision backed by Bloomberg’s group will be received in the broader House, where many Republicans have been highly skeptical of the mayor’s gun control efforts and may seek to transfer the background check money to other areas. The full Appropriations Committee will mark up the spending bill on July 17.

In addition, while the Appropriations subcommittee boosted funding for background checks, it also handed a victory to gun-rights groups by voting to make permanent two annual policy riders related to firearms.

One rider would prohibit the denial of the importation of antique firearms, parts and ammunition, while the other would ban the government from requiring an export license for the sale of firearms and parts to an “end user” in Canada, according to committee staff. The committee also rebuffed a request from Obama to remove an existing rider that prevents the ATF from requiring gun dealers to conduct annual inventories to ensure that firearms are not lost or stolen.

The liberal Center for American Progress criticized the riders and said they would “limit the ATF’s ability to police law-breaking gun sellers.”