"Members of the NRA tend to be very reasonable on this issue," Kelly said, who also appeared on the Fox show.
As Congress responds to the spate of mass shootings in recent years, most notably the December massacre of 20 children and six adults in a school in Newtown, Conn., some are calling for a ban on certain semi-automatic weapons and on high-capacity ammunition magazines. However, calls for expanding background checks appear to have gained the most bipartisan support.
LaPierre said that requiring checks for all gun purchases would be a bureaucratic nightmare.
"It's going to affect only the law-abiding people," he said.
LaPierre was pressed about his contention that gun checks would lead to a national registry, when no one from the Obama administration is calling for that.
"And Obamacare wasn't a tax until they needed it to be a tax," LaPierre said.
Kelly and LaPierre agreed on one point: More people seeking to buy guns illegally should be prosecuted.
"They should be prosecuted and there should be stiff penalties," Kelly said.
A key player in the coming gun debate in Congress, Senate Majority Leader Harry Reid, said on ABC's "This Week" that he's willing to take a look at legislation that would ban certain semi-automatic weapons, but he also noted that he voted against a ban on such weapons in 1994 because it "didn't make sense."
He was more definitive on the issue of background checks, saying "everyone acknowledges we should do something with background checks."
Reid said his goal is for the Judiciary Committee to report out a gun bill. Senators could subsequently seek amendments on the Senate floor. That way, if the bill didn't contain certain provisions, such as the ban on certain weapons, then sponsors would at least get a vote on their proposal and lawmakers would have to go on the record about where they stand.