...In the gun violence debate, she said she believes it would be almost impossible to pass an assault-weapons ban. Even within the Democrats' Caucus there is disagreement on such a ban, but there is growing consensus on limited magazine capacity.
"Where we can make the most difference is with background checks and information shared," she said. "Let's keep guns out of the wrong hands. There's more of a rally around background checks ... and some (Democratic) unity around mental-health issues."
House Minority Leader Nancy Pelosi talks budget, guns, pot in Denver - The Denver Post
Bolded the important parts. As I suspected, they pretty much think they have a lock on the bg checks, and will start pushing a mag ban next.