"We’re looking at background checks and we’re looking at putting everything together in a unified way so that we can have something that’s meaningful,” President Trump told reporters last week in the Oval Office.
“At the same time, all of us want to protect our great Second Amendment," the President added. "It’s very important to all of us."
Mr. Trump made that same point of emphasis in a speech to House Republicans during a party retreat in Baltimore last week.
"Meanwhile, Democrats want to confiscate guns from law-abiding Americans, so they’re totally defenseless when somebody walks into their house with a gun," the President said.
Democrats are also not interested in what they view as a plan which doesn't do enough to curb guns, as Sen. Ted Cruz (R-TX) has urged action on a bill which does more to focus on denying guns to people with a criminal record, or a history of mental health issues - stopping short of background checks on all private gun sales.
"If you have a federal government background check for that, what you will see the next step to be is the only way to enforce that is a federal gun registry and a gun registry is the step you need for gun confiscation," Cruz said in an interview on ABC's "This Week."
Democrats have also been pressing to get the GOP to accept action by the feds to help states with what are called, "Red Flag laws," which can be used to take firearms away from someone who is considered a threat, or has mental health issues.
Many Republicans are opposed to this idea - though it has support from both GOP Senators from Florida, a state which changed its laws after a mass school shooting, in order allow for more opportunities to seize firearms from someone who is considered a threat, or has mental health concerns.