Republican senators in the United States Congress signaled on Thursday that they were hesitant to embrace a call from President Donald Trump for sweeping changes to gun laws, including measures more typically backed by Democrats.

Trump shocked fellow Republicans on Wednesday when he threw his support behind a broad set of restrictions on gun sales in response to the February 14 mass shooting at a high school in Parkland, Florida, that killed 17 people.

But he left the issue in the lap of Congress, and did not say how hard he would twist arms in his party to advance measures that many Americans passionately view as infringing on constitutional right to own guns.

Complicating matters, after meeting with Trump and Vice President Mike Pence late on Thursday, the National Rifle Association’s chief lobbyist Chris Cox said on Twitter that Trump and Pence“don’t want gun control.”

Senate Republican Leader Mitch McConnell said banking legislation – not guns – would be at the top of the agenda next week, and said the process for gun-related bills was still under discussion.

McConnell said he hoped to eventually see debate on a narrowly tailored bill from John Cornyn of Texas, the No. 2 Senate Republican that would strengthen a database of people who are not legally allowed to buy guns.

“We would love to do that at some point. I am hoping there’s a way forward,” McConnell said.

Senate Democrats said they want to debate mandates on background checks at gun shows and internet sales, among other measures, but said Trump would need to push his colleagues.