Do-overs resurrecting legislation that failed the first time are a pretty rare phenomenon in Congress. But Joe Manchin III is predicting that he and Patrick J. Toomey will be able to find the five votes they need to advance their background check expansion proposal a second time around.

A wave of polling in the two weeks since the Senate gun control measure first foundered is offering a decent road map for where to start their search.

Manchin, a West Virginia Democrat, said on Fox News over the weekend that “some confusion” about the measure contributed to its initial defeat. President Barack Obama has gone further, alleging the National Rifle Association and others “willfully lied” in arguing the measure would lead inexorably to a national registry of gun owners.

But if Manchin and his Pennsylvania Republican partner devote some time to educating close-call colleagues about the reach of their proposal, he says, they will prevail. “The only thing that we’ve asked for is that people would just read the bill,” he said. “It’s a criminal and mental background check strictly at gun shows and online sales.”

Whatever their persuasive skills, the pair will also be aided by polling in states represented by some of the last senators who got off the fence and voted against the background check vote.

Public Policy Polling, a Democratic-leaning firm, released results Monday of recent surveys showing declines in the favorability numbers for a handful of senators who signaled they were at least considering a “yes” vote but in the end voted “no.”

In Arizona, background checks were favored by 70 percent but the approval rating for Jeff Flake, who won his seat last fall with just above 50 percent, was pegged at only 32 percent. And, by a 21-point margin, those polled said they trusted John McCain, one of the four GOP senators who voted for the background check measure, more than Flake on gun issues.

In Alaska, both senators’ approval ratings have declined sharply since the last PPP survey in February. Both Democrat Mark Begich, who was one of four red-state Democrats who voted against the legislation and faces a tough battle for a second term next year, and Republican Lisa Murkowski saw their approval ratings slip by 8 points — his to 41 percent and hers to 46 percent.

In Nevada, 46 percent of of voters said they would be less likely to back Republican Dean Heller, who just won a full term, because of his “no” vote.

The new PPP numbers come a week after the firm released a poll showing 75 percent support for background checks in New Hampshire but a 15-point plunge in the approval rating for Republican Kelly Ayotte from October to when she voted against the background check language.