The Senate won't discuss gun control measures this week, top Democrat Dick Durbin said.
Tuesday's deadly mass shooting in Uvalde, Texas, sparked renewed calls for gun control.
Sen. Schumer also blamed Republican colleagues for being "unwilling to do what it takes to keep Americans safe."
Top Democrat Dick Durbin said on Tuesday that the Senate won't discuss gun control measures until after the upcoming holiday weekend.
"It's too late to prevent the last shooting. We've already failed those victims and families," the Illinois senator said. "We need to act to prevent the next shooting. We need to identify the risks and threats and finally do something."
Durbin also said that Senate Majority Leader Chuck Schumer began the Rule 14 process for a background check bill on Monday night, which would allow the Senate to put the bill directly on the Senate calendar.
"We're going to have a chance to debate that and to vote on the floor when we return from Memorial Day," Durbin said. "The House of Representatives already passed a bill on this. I think it's time for the Senate to vote on it."
Schumer on Tuesday called gun violence a "plague," and expressed skepticism that Democrats and Republicans could come together to advance gun control legislation.
In a speech on the Senate floor, he blamed his Republican colleagues for being "unwilling to do what it takes to keep Americans safe." Axios reported that he has also signaled that he wouldn't force a vote before senators leave town this weekend.
Tuesday's mass shooting at an elementary school in Uvalde, Texas - that left 19 children and two adults dead - sparked renewed calls from Democrats and gun-control advocates for more firearms restrictions at a state and federal level.
Republican Sen. Lindsey Graham left the door open to debating gun control measures, while other GOP members like Sen. Ted Cruz called for more guns and security at schools.
President Joe Biden issued his own plea for gun control in a late-night emotional address on Monday.
"The gun lobby has spent two decades aggressively marketing assault weapons," he said, calling for restrictions on assault weapons.
Meanwhile, former President Barack Obama slammed Republicans and the gun lobby for showing "no willingness to act in any way that might help prevent these tragedies."
The Uvalde shooting was the deadliest at an elementary school since Sandy Hook in 2012.