Although the Senate in April blocked a bipartisan proposal to expand background checks, Senate Majority Leader Harry ReidHarry ReidRepublican failure Senate about to enter 'nuclear option' death spiral Top GOP senator: 'Tragic mistake' if Democrats try to block Gorsuch MORE (D-Nev.) has vowed to reconsider the bill before the end of the year. Meanwhile, advocates are using the Newtown anniversary as a platform to redouble their pressure on Congress to revisit the issue.

As a part of that effort, New York City Mayor Michael Bloomberg (I) this week asked wealthy donors to withhold funds from the Senate Democrats who opposed the background check bill in April. And the families of Newtown victims met with Speaker John BoehnerJohn BoehnerPaul Ryan sells out conservatives with healthcare surrender Matt Schlapp: 5 lessons Trump, Ryan must learn from healthcare debate Nunes rebuffs calls for recusal MORE (R-Ohio) and Minority Leader Eric CantorEric CantorPaul Ryan sells out conservatives with healthcare surrender A path forward on infrastructure Democrats step up calls that Russian hack was act of war MORE (R-Va.) Wednesday to urge tougher laws.

Hoyer said BoehnerJohn BoehnerPaul Ryan sells out conservatives with healthcare surrender Matt Schlapp: 5 lessons Trump, Ryan must learn from healthcare debate Nunes rebuffs calls for recusal MORE agreed to the meeting because “he is an empathetic person” who wants to show respect for people who have suffered great loss.

“But I don't know that they will move him to action,” Hoyer added.

Behind Boehner, GOP leaders have said for months that they would wait for the Senate to act before considering new gun laws in the lower chamber. But Rep. Bob GoodlatteBob GoodlatteMoving Copyright Office authorities to executive branch could improve accountability Register of copyrights should be presidential appointee Week ahead: Senate takes aim at Obama-era 'blacklisting' rule MORE (R-Va.), chairman of the Judiciary panel, which has jurisdiction over gun laws, told The Hill last month that he's had “a lot of discussions” with Boehner on the topic, suggesting the House might tackle the issue independent from the Senate.

“We are trying to improve the system to keep people who are barred under the law from owning firearms from getting access to them,” Goodlatte said. “We don't think the things that were proposed in the Senate do that. So we have not backed away from trying to figure out how to improve that, but we've made no decisions yet about what to do.”

Advocates are hoping that public opinion polls — which show support for expanded background checks — will force opposition lawmakers to rethink their position. Two new surveys released Wednesday by Bloomberg's group, Mayors Against Illegal Guns, found that voter discontent with Sens. Jeff FlakeJeff FlakeObama FCC's 'privacy' rules were a sham Wounded Ryan faces new battle Overnight Tech: High court hears case on where patent suits are filed | House to vote on blocking internet privacy rules | Facebook's new tools for voters MORE (R-Ariz.) and Kelly AyotteKelly AyotteFEC commissioner to Trump: Prove voter fraud Live coverage: Day three of Supreme Court nominee hearing Lewandowski saw no evidence of voter fraud in New Hampshire MORE (R-N.H.) continues to grow two months after they opposed the background check bill.

“Both senators have suffered for their votes against legislation that is overwhelmingly supported by Arizona and New Hampshire voters,” the survey results claim.

To pass the background check bill, Reid would need the support of five additional senators to defeat a likely GOP filibuster.

Hoyer, for his part, is pessimistic the House would act even if Reid is successful.

“I would hope that they would move it here, but I don't see any indication that the Republican leadership — even Mr. Boehner or Mr. Cantor or Mr. Goodlatte — has any intention of doing something,” Hoyer said. “We will see.”