National Rifle Association spokeswoman Dana Loesch complained Sunday about efforts to “find daylight” between her organization and President Trump, but the reality is that daylight exists. Trump said last week that he wants to expand background checks for gun buyers, raise the minimum purchase age to 21 and ban bump stocks, which enable semiautomatic weapons to mimic the rapid-fire capabilities of fully automatic guns.

The NRA has signaled opposition to all three proposals.

Trump and the NRA do have something in common on these points: Each appears to view the other as persuadable.

“There is nobody that loves the Second Amendment more than I do, and there is nobody that respects the NRA [more],” Trump said Friday at the Conservative Political Action Conference. “They’re friends of mine. … But we really do have to strengthen up — really strengthen up — background checks. We have to do that.”

Two days later, on ABC’s “This Week,” Loesch said, “These are just things that he’s discussing right now.”

Enter “Fox & Friends,” the Fox News morning show that often validates Trump but occasionally attempts to redirect him. Last month, for example, the show questioned the wisdom of Trump's support for a federal surveillance program — and appeared to prompt the president to reconsider his stance.

Trump frequently tweets along with “Fox & Friends,” and Steve Doocy, Ainsley Earhardt and Brian Kilmeade revel in hosting “the most powerful TV show in America,” as the New York Times’s James Poniewozik described the program last year.

The position of “Fox & Friends” matters because it could influence the president's thinking. And the position of “Fox & Friends” is that background checks for gun buyers ought to include more information than they currently do — information such as the dozens of times the school shooter in Parkland, Fla., had a run-in with law enforcement but was not arrested.

“Why is that not included in a background check?” Kilmeade said Monday. “Who is safer by not including this abhorrent behavior on a background check? So the police reports, the arrivals — at the very least, alert local sheriffs that this 18-year-old wants to buy an AR-15, and then the sheriff gets a call from the gun shop owner, and he says, 'Yeah, whatever you do, don’t sell Nikolas Cruz that gun.’ And maybe it stops him in his tracks.”

The hosts continued from there:

EARHARDT: I don’t think that’s political. I think Republicans and Democrats would agree with that.

KILMEADE: I hope so.

EARHARDT: If you have dozens — if the cops have come to your house dozens of times, you’re slamming your mom against the wall and putting a gun to her or whatever, that needs to be on your report. Same with all that stuff he posted on social media. That needs to be on his report.

KILMEADE: That he was cutting himself.

EARHARDT: Yeah. And doing all that to animals.

KILMEADE: Bringing a dead bird to class and holding it there.

Kilmeade went on to say that putting every police encounter on a background check could be problematic. He presented a hypothetical scenario in which one spouse, in the midst of a messy divorce, might call the police on the other spouse out of spite rather than because of a real threat.

“That’s the bad part,” Kilmeade said. “But the good part is we err on the side of safety, so the next kid who’s 18 years old and out of control, with multiple alerts on his background that he’s going to kill somebody quickly, they get stopped.”

Later in Monday’s telecast, the hosts interviewed Eric Trump, the president’s son.

“What about the NRA?” Earhardt asked. “Should they give a little bit?”

“Listen, at the end of the day, I think the NRA will,” Trump replied.

That might be wishful thinking on Trump’s part, but the NRA could have a harder time talking the president out of tougher gun regulations if he is getting positive feedback on his plan from “Fox & Friends.”