Keeping up a Democratic drumbeat of criticism of GOP leaders in Congress in the wake of mass shootings in El Paso, Texas and Dayton, Ohio, House Speaker Nancy Pelosi on Wednesday called for the GOP Senate to act on a House-passed bill to expand background checks to all private gun sales, as Pelosi held out the possibility of other gun votes this fall as well.

"We've sent our legislation to the Senate," Pelosi told an audience of Democrats in Illinois, as she pointed the finger at Senate Majority Leader Mitch McConnell.

"Moscow Mitch says that he is the grim reaper," Pelosi said of McConnell's refusal to take up a series of bills approved by Democrats in the House.

"All of this legislation is alive and well," Pelosi countered to applause, as she said that 'high capacity magazines should be eliminated as well.'

"We can, we should, we must act to address the gun violence epidemic in this country," said Sen. Chris Coons (D-DE).

Politico reported that White House aides would go to the President's golf retreat in New Jersey in coming days to discuss the issue of gun legislation - but at this point there is nothing scheduled in the Senate.

Still, there were signs of discussions, as President Trump said Tuesday that he had a conversation with Sen. Chris Murphy (D-CT), one of the prime supporters of expanded background checks legislation.

But there was no hint of a new deal on guns, as one GOP Senator who was in Washington on Tuesday - Sen. Mike Rounds (R-SD) - gave no indication that Republicans were anywhere near accepting new federal legislation on 'Red Flag' laws.

"It has to be something which is effective, and will actually withstand Second Amendment challenges," Rounds told reporters at the U.S. Capitol.

Often, Rounds will often stop and talk to reporters in the Capitol at length - but on this occasion, it was obvious the South Dakota Republican wanted to get back to his office right away, as he hopped into a waiting elevator, and then on the underground subway.