House Speaker Paul Ryan showed little interest Tuesday in some of the stricter gun proposals being floated by President Donald Trump or bipartisan coalitions in Congress, as Senate Republicans pushed a more modest measure to boost the existing background check system with new penalties and incentives.

As student survivors of the Marjory Stoneman Douglas High School shooting roamed the Capitol for a second day, promoting tougher gun laws in meetings with top lawmakers, Ryan acknowledged “system failures” in Florida that he said Congress should review. But GOP leaders stopped short of offering new legislation beyond the background check fix.

“We shouldn’t be banning guns for law-abiding citizens,” Ryan told reporters. “We should be focusing on making sure that citizens who should not get guns in first place don’t get those guns.”

The Senate was poised to consider legislation from Sens. John Cornyn, R-Texas, and Chris Murphy, D-Conn., to strengthen the National Instant Criminal Background Check System, though votes were not yet scheduled amid resistance from within the GOP ranks.

The “Fix NICS” bill, similar to one approved last year in the House, would penalize federal agencies that don’t properly report required records used to determine whether someone can legally buy a gun.

“Let’s do what we can and build from there,” Cornyn said.

But broader proposals were quickly circulating, and Senate Minority Leader Chuck Schumer, D-N.Y. urged the Senate to be more ambitious than the “tiny” Fix NICS bill in its response to the Parkland, Fla., assault that left 17 dead.

Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa., are reviving their background check bill, which would expand checks to include purchases online and at gun shows. It had failed after the Sandy Hook Elementary School shooting in 2012. And Sen. Susan Collins, R-Maine, and Sen. Heidi Heitkamp, D-N.D., pushed an effort to block terror suspects on the federal no-fly list from buying guns.

“Let’s not set our sights too narrow and squander this moment,” said Schumer, who also met with students Tuesday. “Let’s try for significant, bipartisan legislation that will make a real difference in keeping our children safe.”

Cornyn said he was dismayed that senators wanted to debate other ideas before taking up the background checks bill, and urged the chamber to immediately pass it.

“If our attitude is, ‘I want everything on my list or nothing,’ we’re going to end up with nothing,” he warned.

The efforts in Congress comes as Trump has floated his own shifting ideas on gun safety, including a proposal for arming teachers that has support from the National Rifle Association, but few backers on Capitol Hill.

Trump declared Monday he’s willing to take on the NRA over gun legislation, and chided lawmakers not to fear the gun lobby. But the Republicans who control Congress weren’t so sure.

“You guys, half of you are so afraid of the NRA,” the president said Monday at a meeting with the nation’s governors. “There’s nothing to be afraid of. And you know what? If they’re not with you, we have to fight them every once in a while. That’s OK.”

One plan, to prohibit sales of bump stocks —— the devices that turn rifles into automatic-style weapons and were used in the Las Vegas mass shooting last fall —— was under consideration at the Justice Department.

Attorney General Jeff Sessions said top officials believe the hardware can be banned through the regulatory process. This was the approach preferred by the NRA and it could relieve Congress of pressure for legislative action. The federal Bureau of Alcohol, Tobacco, Firearms and Explosives previously said it was powerless to restrict the devices without action from Congress.

Though Trump on Monday did not mention his earlier idea for increasing the minimum age for rifle purchases, he said he wants to toughen the Cornyn bill with stricter background checks, a change the NRA has opposed.

“We’re going to strengthen it,” Trump said. “We’re going to make it more pertinent to what we’re discussing.”

Democrats have long pressed for more sweeping changes toward a universal background check system, including requiring inquiries for online and gun show purchases.

In the House, many Democrats — and a few Republicans — also want to reinstate an assault weapons ban that expired more than a decade ago.

Rep. Brian Mast, R-Fla., a wounded Afghanistan war veteran, said he described his proposal to ban assault weapons to his House GOP colleagues Tuesday at a closed-door meeting. “There was not thunderous applause,” he said.

The House passed legislation in December that included changes to the background-check system. It was part of a broader package that stalled in the Senate because it included expanded gun rights by requiring states to recognize conceal-carry permits issued by other states.

The House package also included a measure to study bump stocks after the Las Vegas assault, the deadliest mass shooting in U.S. history.

In the Senate, Republican leaders see the best route to passage in separating the issues of background checks and state reciprocity measures.

The more narrowly tailored “fix NICS” was introduced last fall after the shooting of churchgoers in Texas. At the time, authorities acknowledged having failed to report the Texas gunman’s domestic violence conviction to the database.

But even the “Fix NICS” bill faced resistance from some in the GOP ranks.

Sens. Mike Lee of Utah and Rand Paul of Kentucky said the bill would encourage federal agencies “to encroach upon constitutionally guaranteed rights without affording robust due-process protections.”

(AP)