Gun control advocates on Capitol Hill, who earlier this month suffered a serious setback in the Senate, are hoping to revive the divisive issue, pointing to new polls that continue to show widespread public support for some gun restrictions.

Advocates said they remain particularly optimistic about a bipartisan compromise that would expand background checks for gun buyers, the same proposal that failed in the Senate on April 17 after falling six votes short of the 60 it needed to advance.

Polls taken after the Senate voted show public support for background checks remains high, while approval ratings dropped for some Republicans who opposed the bill, including Sens. Jeff Flake of Arizona and Kelly Ayotte of New Hampshire.

"Senators who voted against background checks have seen approval ratings decline, and in a couple of cases, those declines are very substantial," said Tom Jensen, director of the Democratic-leaning Public Policy Polling, which conducted one of the surveys.

Jensen's poll, along with data released Monday by Gallup, signals that Americans remain eager to reduce gun violence months after a gunman killed 20 children and six adults at a Connecticut elementary school.

About 83 percent of those polled by Gallup support expanding background checks for gun buyers.

The PPP poll, meanwhile, showed that some of the Republican senators who voted against the background checks saw their approval ratings drop. About 52 percent of Arizona voters say they're now less likely to support Flake because he opposed the measure, the poll shows. Background checks are supported by about 70 percent of Arizonans.

Sen. Joe Manchin, D-W.Va., who worked with Sen. Pat Toomey, R-Pa., to craft the compromise on background checks, said he expects the measure to pass on its second try because he's going to offer the background check proposal separately from a tougher gun control bill that would also ban assault weapons and reduce ammunition magazines -- two proposals widely opposed by Republicans and red-state Democrats.

But it won't be easy to get a bill to the floor again. Manchin has for now lost the backing of Toomey, who was seen as key to attracting Republican support.

"Sen. Toomey has said a few times that the Senate has spoken on this issue," Toomey spokeswoman E.R. Anderson said Monday. "He came up six votes short. There would have to be a change in the atmosphere to yield a different outcome. That seems unlikely in the near future."

The lack of Republican support would make it harder to pass the background checks because Democrats control only 55 of the 60 votes they need. A second vote also could put several of their own vulnerable members from pro-gun states in a difficult political position for a bill that stood little chance of passing.

Democratic Sens. Mark Pryor of Arkansas, Mark Begich of Alaska, Max Baucus of Montana and Heidi Heitkamp of North Dakota all voted against the Toomey-Manchin bill and will likely do so again.

Senate Majority Leader Harry Reid, D-Nev., has so far been unwilling to commit to a firm date on taking up a new measure.

Reid said Democrats "are working on a path forward ... but we are not ready to move on that at this time."