Ryan, R-Wis., speaking as Congress returned from a long break after the February 14 killing of 17 students and teachers by a former student armed with an AR-15 rifle, said decisions about teachers' use of weapons should rest with local authorities.
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.
"As a parent and as a citizen, I think it's a good idea, but as speaker of the House I think we need to respect federalism and respect local jurisdictions", he said.
"We do know there are gaps in the background check system that need to be plugged", he said.
Ryan interrupted and did not let her finish the question.
"If our attitude is, 'I want everything on my list or nothing, ' we're going to end up with nothing", he warned. Since that tragic event, a student-led movement has been rallying support for changes to gun laws. In particular, the Federal Bureau of Investigation had not followed up on tips, and local school resources officers at the school had failed to protect students, he said.
Asked about proposals for stricter background checks or barring assault weapon sales, Ryan says Congress shouldn't be "banning guns from law-abiding citizens". What about law enforcement?
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".
It would also penalize federal agencies that don't upload the records by, for example, withholding certain bonus pay for political appointees.
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Many observers expected Trump would replace Jacobson at some point and bring in someone who more closely shares his views. Former Secretary of State John Kerry tweeted a message of thanks.
Even as that measure has doubtful prospects in Congress, Republicans controlling both houses stand at odds on other, related legislation.
At a press conference on Tuesday, his first since the school shooting in Florida two weeks ago in which 17 people died, House speaker Paul Ryan indicated his opposition to further restrictions on gun ownership.
The House approved the bill late previous year as part of a broader package that also expanded gun rights by requiring states to recognize conceal-carry permits issued by other states. Ryan signaled it would be back to the drawing board if the Senate - which is not expected to vote on the House bill - declines.
"I think what angered me the most is that there was a sheriff's deputy trained and armed at the school, assigned to protect the school, and he hid out instead of protecting those students and confronting the shooter", Mr Scalise said.
Authorities said the gunman would have been denied a firearm if the Air Force had reported his court-martial and discharge over domestic violence charges. "We expect that to be a topic of discussion".
Ryan said he hopes the Senate will take up the bill aimed at strengthening the background check database passed by the House in December, adding the lower chamber also passed mental health reform legislation he hopes will help prevent future mass shootings.
Schumer called for wide-ranging gun-control legislation, including the closing of loopholes.
Trump and a host of bipartisan lawmakers support Legislation improving NICS but many Democrats have said the proposal is only the first step in addressing gun violence and have insisted on more expansive approaches.