WASHINGTON — Democrats who vowed a crackdown on guns after the horrific Newtown, Conn., school shooting are touting prospects for Senate passage of expanded federal background checks, even as they acknowledge there isn’t enough support to restore a ban on assault-style weapons.

Senate Majority Leader Harry Reid said Thursday that a measure likely to be debated in his chamber next month will include tougher laws and stiffer sentences for gun trafficking and increased school safety grants.

Closing background check loopholes will be the core of the legislation, just as it was the cornerstone of President Barack Obama’s proposals for stemming gun violence following the December slayings of 20 first-graders and six staffers at Sandy Hook Elementary School in Connecticut.

Including expanded checks in the gun legislation signals that Democrats feel they can win bipartisan support for the measure or are happy to dare Republicans to reject the entire gun-control package and face political consequences in next year’s elections.

Reid, D-Nev., said he hoped a trio of senators would craft a bipartisan background check compromise. If not, he said, senators would consider a stricter version that allows fewer exemptions approved by the Senate Judiciary Committee on a party-line vote.

“This moves the ball forward on gun safety in the Senate,” said Sen. Chuck Schumer, D-N.Y., one of the senators hunting a background check deal.

Schumer said he hoped an accord could be ready when the Senate returns from its upcoming two-week spring break. Moderate Sens. Joe Manchin, D-W.Va., who has an A-rating from the National Rifle Association, and Mark Kirk, R-Ill., are also involved.

The background check system is aimed at preventing criminals and others from acquiring firearms. It currently applies only to sales by federally licensed gun dealers, not private transactions at gun shows or online.

The fate of the overall legislation remains uncertain, with Democrats all but sure to need Republican support for it to survive. Action would then shift to the GOP-run House, where leaders have shown no taste for expanding background checks for private purchases.

Earlier, Reid decided to exclude a proposed assault weapons ban from the bill, fearing it would sink the legislation, but will allow a vote on the plan as an amendment. The ban’s sponsor, Sen. Dianne Feinstein, D-Calif., seems sure to lose due to opposition from Republicans and moderate Democrats.

An Associated Press-GfK poll showed more than 8 in 10 people support broadening the background check requirement to gun shows. Other surveys show similar overwhelming support.

Critics appeared unbowed. The NRA and others say criminals ignore background checks in getting guns illegally, and warn the expansion would lead to a federal registry of gun owners.

“We remain as committed as we have been to opposing gun bans,” said Andrew Arulanandam, an NRA spokesman. He declined to comment on a potential compromise but said if the Senate considers Schumer’s version of background checks, “we will do whatever we can to defeat it.”

The NRA wants Congress to fund more armed guards at schools, step up prosecutions of people who file false gun applications and increase the background check system’s access to state records of people with mental and other problems.

Sen. Charles Grassley of Iowa, top Republican on the Senate Judiciary Committee, said of Reid’s announcement, “I don’t know how the leader expects members to vote on an ever-changing piece of legislation that has yet to gain bipartisan support.”

In a hint of possible movement, one option that Schumer, Manchin and Kirk are considering would require background checks and record-keeping for private sales at gun shows and commercial sales online. It would exclude in-person, noncommercial transactions between people who know each other.

Other exclusions could include gun transactions between relatives and acquisitions by people with state-issued concealed carry permits, and there would be an online background check system for people in remote areas.