Senate Democrats said Tuesday they’ll push the gun debate to the full Senate floor in April, though they dealt a major blow to gun control advocates when they decided not to include bans on sales of so-called assault weapons and high-capacity ammunition magazines in the main bill.

Sen. Dianne Feinstein said she’ll still try to offer both bans as amendments during the floor debate, but acknowledged it would have been easier if they’d been included in the bill itself.

The decision is also a loss for President Obama, who called for a ban on military-style semiautomatic weapons and on high-capacity magazines after the December shooting rampage in Newtown, Conn.

But Senate Majority Leader Harry Reid said adding in Mrs. Feinstein’s proposal would have hurt chances to get anything done this year.

“I’m not going to try to put something on the floor that won’t succeed,” the Nevada Democrat told reporters. “I want something that will succeed. I think the worst of all worlds would be to bring something to the floor and it dies there.”

Mr. Reid informed Mrs. Feinstein, California Democrat, on Monday that her legislation would not be part of the package.

“I tried to make the case for it, and he indicated we would have a separate vote,” Mrs. Feinstein said. “Obviously I’m disappointed. … The enemies on this are very powerful. I’ve known that all my life.”

White House Chief of Staff Denis McDonough wasn’t ready to throw in the towel, saying the administration will try to rally the votes to pass the weapons ban.

“We’re going to work on this. We’re going to find the votes,” he said on CNN on Tuesday afternoon. “And it deserves a vote — we’ll see if we can get it done.”

Mr. Reid, though, said Tuesday that Mrs. Feinstein’s measure, “using the most optimistic numbers,” has less than 40 votes.

The assault weapons ban would renew the prohibition that existed from 1994 through 2004. It would apply to semiautomatic weapons that have military-style add-ons such as folding stocks or pistol grips.

The magazine ban would apply to those capable of carrying more than 10 rounds. Its backers say lives could be saved if shooting spree killers had to stop to reload, while opponents say there are already so many magazines in circulation that a ban would be useless, and would likely hurt law-abiding citizens.

Mr. Reid said he wants to bring legislation to the floor as soon after Congress’ Easter break as he can, which would be roughly early to mid-April, but it’s still unclear exactly what will be in the main bill.

In addition to the assault weapons ban, three other bills have cleared committee: one requiring background checks on virtually all gun sales, another to crack down on straw purchasers and gun trafficking, and another on school safety.

The background check bill is the most contentious of those three, and lawmakers are still working behind the scenes to find a compromise that can garner 60 votes in the chamber.

Sen. Joe Manchin III, a West Virginia Democrat who has been trying to work out a compromise, said Tuesday he was optimistic on that front.

“I’m still working very hard, and hopefully reasonable people will look at reasonable proposals and something will happen,” he said.

Currently, all sales by licensed firearms dealers must go through background checks, but transactions between private individuals do not. Lawmakers are looking for a way to extend checks to almost all transactions without also creating a record-keeping system that gun rights supporters fear could turn into a gun registry.

The background check bill, like Mrs. Feinstein’s assault weapons legislation, cleared the Judiciary Committee on a 10-8 party-line vote.

The school safety measure received broad support while the gun trafficking bill passed 11-7, with only Republican Sen. Chuck Grassley of Iowa voting with the Democrats.

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