Washington — President Donald Trump stopped short on Monday of a full-throated endorsement of any legislative proposals to tighten gun restrictions while lawmakers insisted that the fate of any changes lay in the president’s hands.

While Senate leaders explored the possibility of passing a modest improvement to the national background-check system for firearm buyers, House action was uncertain, and Trump again turned attention away from guns and toward the various security breakdowns that preceded the Feb. 14 rampage inside Marjory Stoneman Douglas High School in Parkland, Fla., that left 17 dead.

Hosting dozens of governors at the White House on Monday, Trump reserved his harshest criticism for a local sheriff’s deputy who remained outside the school while Nikolas Cruz, the alleged shooter, targeted his former classmates and faculty members.

“You don’t know until you test it, but I think – I’d really believe I’d run into (the school), even if I didn’t have a weapon,” Trump said, telling the assembled governors that he thought they, too, would have rushed inside.

He did not, however, throw his support squarely behind any particular legislative proposal on Monday, including measures he previously floated that would raise the minimum purchase age for rifles, mandate comprehensive background checks for gun buyers and ban “bump stocks,” which allow widely available semiautomatic rifles to fire like fully automatic guns.

Instead, Trump trumpeted his close ties to the leaders of the National Rifle Association, and he predicted that the powerful gun rights organization would “do something” to respond to the escalating concern nationwide about guns.

“Don’t worry about the NRA,” Trump said. “They’re on our side.”

In the wake of the shooting, a growing movement led by student survivors and parents has demanded tighter restrictions on firearms and pressured Trump and Congress to reject the NRA. Several lawmakers and governors — including Florida Gov. Rick Scott, a Republican weighing a U.S. Senate bid — have shifted away from NRA policy priorities and endorsed some hardening of state gun laws.

But a divided Congress that has a long track record of inaction after previous mass shootings is struggling to agree on any significant step with primary season getting underway.

“These are feel-good measures that aren’t going to solve the problem,” said Sen. Steve Daines, R-Mont., referring to age limits, bump stock bans and universal background checks.

The Senate could move on one modest but bipartisan gun measure backed by the NRA, the Fix NICS Act, which would create additional incentives and penalties to ensure that agencies report pertinent data on potential gun buyers to the National Instant Criminal Background Check System.

The bill was written to plug gaps exposed by the November killings of 26 churchgoers in Sutherland Springs, Texas, perpetrated by a man who would have been prevented from purchasing his weapons had the Air Force properly reported a 2012 domestic violence offense to the database.

Two Republican senators, Mike Lee, Utah, and Rand Paul, Ky., have registered objections to bill, warning that it “could lead to the denial of constitutional rights without due process.” A spokesman for Lee said on Monday that he had placed a hold on the bill, blocking its rapid consideration.

It is unclear whether the House, which is scheduled to end its workweek today, would pass the bill as a stand-alone measure.

House lawmakers passed the Fix NICS Act in December, but as part of a bill that would require states to recognize concealed-carry permits from other states – a measure favored by the NRA but strongly opposed by gun-control advocates.

House Majority Leader Kevin McCarthy, R-Calif., appearing Monday on the Fox Business Network, called for action on background checks but did not specify whether he would bring the stand-alone NICS bill to the floor.

A bill aimed at beefing up background checks, first proposed in 2013 by Sens. Joe Manchin, D-W.Va., and Patrick Toomey, R-Pa., could be revived, the two men said, but they maintained that Trump’s support was a prerequisite.

“President Trump has to find a pathway that he feels comfortable with,” Manchin said in a Monday radio interview on West Virginia’s MetroNews network.

The Manchin-Toomey measure would mandate background checks for all gun sales between private parties, with exceptions for family members. Under current law, only federally licensed dealers must run checks, leaving many transactions exempt, including many conducted at gun shows and online.

Senate Minority Leader Chuck Schumer, D-N.Y., said on Monday that “at the very least” Congress should pass legislation mandating universal background checks, similar to Manchin-Toomey, in response to the Parkland shooting.

“My Republican friends face a simple choice: Do something real on guns, or please the NRA. Doing both is impossible,” Schumer said.

There appeared to be waning enthusiasm among Republicans, and some Democrats, for a measure more closely tailored to the circumstances surrounding the Parkland shooting: a higher minimum age for rifle purchases.

Cruz, 19, bought his AR-15 rifle from a licensed dealer, passing a background check. Currently, long guns can be purchased at 18; some policymakers have floated raising the limit to 21, the current federal law for handgun buyers.

The NRA opposes raising the age limit, and lawmakers of both parties — including Manchin — have expressed concerns, often citing the fact that tens of thousands of 18- to 20-year-olds are entrusted with firearms as members of the military.