Gun control supporters scrambled to find 60 votes to pass expanded background checks on firearms purchases, hoping to sway reluctant senators ahead of a showdown vote.

After spinning its wheels for most of the day Tuesday, the Senate set up a series of gun votes for Wednesday, including what has become the critical fight — a proposal to expand background checks to include all sales at gun shows and over the Internet, though it would exclude person-to-person private sales.

Senate Majority Leader Harry Reid, Nevada Democrat, has scheduled votes on eight other amendments to underlying gun legislation, including bans on certain types of guns and magazines.

He told reporters earlier Tuesday that gun control supporters were still searching for support, but he felt they had momentum.

“Am I saying it’s all over with, done, we got the votes? No, but we certainly feel we have the wind at our back,” he said.

Sen. Richard Blumenthal, Connecticut Democrat, said the votes offer an opportunity to “keep faith” with the families of the 20 children and six adults killed at Sandy Hook Elementary School in Newtown, Conn., and the 3,400 victims of gun violence since the tragedy.

“Just as the world has watched Newtown since Dec. 14, Newtown will be watching the U.S. Senate [Wednesday],” he said. “It will mark a critical milestone in the movement to fight gun violence.”

But the delay in voting seemed to signal momentum was on the other side — a sense buttressed by the dwindling number of undecided lawmakers and the growing number of those who say they cannot vote for the background check proposal.

“The majority doesn’t have the votes to pass their own amendment, so we’re not voting,” said Sen. Chuck Grassley of Iowa, the ranking Republican on the Judiciary Committee. “If we turn to assault weapons or magazines, then it’s clear to all that the majority knows the votes aren’t going to be there.”

The Senate last week agreed to bring the gun bill to the chamber floor, with many Republicans supportive of that move. Since then, however, the bill has stalled and lawmakers have not voted on any amendments.

Earlier in the day, Democrats got a boost from the presence of former Rep. Gabrielle Giffords, Arizona Democrat, who was gravely wounded when a gunman opened fire at an outdoor town hall she was holding in Tucson in 2011. Democrats also heard an emotional plea for action from Sen. Joe Manchin III of West Virginia, a co-sponsor of the background check compromise, as well as Sens. Richard Blumenthal and Christopher Murphy of Connecticut and Tim Kaine of Virginia, who was governor of the state at the time of the Virginia Tech shootings in 2007.

The underlying bill has language on background checks that the compromise is supposed to replace.

Other amendments up for a vote Wednesday would ban so-called assault weapons and high-capacity magazines.

Mr. Grassley, Sen. Ted Cruz of Texas and other co-sponsors plan to unveil their substitute amendment Wednesday morning that makes changes to the National Instant Criminal Background Check System, provides resources to help address mental health and school safety, protects veterans from false health determinations, and addresses gun trafficking and straw purchasing.

The wide array of amendments could be a double-edged sword for Democrats. Voting against provisions to ban military-style, semi-automatic rifles and high-capacity ammunition magazines — measures widely presumed to fail — could give wary senators a chance to shore up their pro-gun bona fides and still vote for expanded background checks.

But Republican amendments also could attract on-the-fence senators who represent gun-friendly states and make the background check amendment — already facing problems attracting the 60 votes necessary to avert any filibuster — that much more difficult to pass.

The background check amendment carves out exemptions for private transactions between family members and friends. Presently, only federally licensed dealers are legally required to perform the checks.

A total of 68 senators voted to bring the bill to the Senate floor for debate, including 16 Republicans. But of those GOP members, just four have indicated they could support the Manchin-Toomey background check proposal, while 11 have said they will oppose it.

Sen. Kelly Ayotte of New Hampshire has not signaled publicly whether she will vote for it.

Several Democrats also could vote against the background check compromise, which — combined with the GOP objections — would leave the measure shy of the 60 votes needed.

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