Kelly said he and his wife reached out to Heller to discuss a poll they commissioned that found 80 percent of Nevada voters were unaware of Heller's position on a gun background check bill.

"If you look at our polling data, it seems that it would be in his favor, if it came up again, to vote for" the bill, Kelly said according to the Las Vegas Review-Journal.

The poll found that, since voting against the background check bill in April, 40 percent of Nevada voters are less likely to support Heller's reelection.

Kelly said he and Giffords, who suffered a gunshot wound to the head during a shooting rampage in 2011, tried to meet with Heller to discuss the findings.

"We contacted him about looking at these numbers, and he wasn't interested," Kelly said.

Kelly suggested that Heller did not want to meet because it could anger the NRA.

"That's a hard thing to calculate," Kelly said. "I mean, how do you balance what your constituents want with how much money is going to be spent against you in your next election?"

A Heller spokesman said that Heller's stance on gun restrictions had not changed in the past few months, according to the Review-Journal. The bill Heller voted against expanded background checks to sales over the Internet and at gun shows. Heller, in April, said he worried that the bill "could lead to the creation of a national gun registry and puts additional burdens on law abiding citizens." 

Since the shooting where Giffords suffered the gunshot wound, Giffords and Kelly founded Americans for Responsible Solutions, a group that advocates strengthening the nation's gun laws. Giffords and Kelly visited Nevada on Monday during a seven-state swing to rally support for passing new gun laws.