From Washington Post, "Trump's openness to extensive background checks for gun buys draws warning from NRA":

President Trump has repeatedly told lawmakers and aides in private conversations that he is open to endorsing extensive background checks in the wake of two mass shootings, prompting a warning from the National Rifle Association and concerns among White House aides, according to lawmakers and administration officials. 

Trump, speaking to reporters Wednesday before visiting Dayton, Ohio, and El Paso, where weekend shootings left 31 dead, said there "was great appetite for background checks" amid an outcry over government inaction in the face of repeated mass shootings.

While there is no reason to give the jackals even an inch, a background check only bill sounds a lot better than the his list of demands on Monday, which included "red flag" gun seizure laws, swift executions for so-called "hate crimes," "involuntary confinement" for people the state deems "mentally disturbed," and directing the DOJ to work with states, local law enforcement and social media sites to "detect mass shooters before they strike."