The initiative is being pushed by families of last year's Columbine High School shootings, who are also pushing to bring the agenda to the national table, said SAFE Colorado spokesman Tom Mauser.
"Once Colorado gets this through, it will have the attention of the nation and we'll see this happen," Mauser, who lost his son 15-year old son, Daniel, in the Littleton shooting, said Wednesday on CBS News' The Early Show. "I think Congress will finally act on it."
The state's Supreme Court rejected Tuesday an attempt by the gun lobby to keep off the Nov. 7 ballot an initiative that would close the so-called "gun-show loophole."
Mauser said they have the 62,300 signatures they need to get the initiative on the ballot, but will try to get 40,000 more to make up for any signatures ruled invalid.
"We'll have challenges from the gun lobby on that process, the petition process," Mauser said. "But once we're through that, and get it on the ballot, we have to get the Coloradans who support it now to hang in there and vote for this initiative."
While Mauser claimed 80 percent of Colorado residents support the measure, gun-rights advocate Dudley Brown said challenges to the initiative would continue.
"We will fight the signatures they get," said Brown, head of Rocky Mountain Gun Owners. "We don't believe it was legal to gather signatures before the Supreme Court had ruled and the language was set."
The country's largest pro-gun lobbying group, the National Rifle Association, has remained relatively quiet on the state issue.
"They see those poll numbers - why 80 percent of Coloradans support this consistently on a state-wide basis," Mauser said. "They may count on their local affiliate to carry the burden and not have their name up front. But this is the call of the people."
Currently, only people buying guns from federally licensed gun dealers have to undergo criminal background checks at gun shows. Sales by private dealers are exempted. The initiative would require background checks for all sales at gun shows.
In its ruling Tuesday, the Colorado Supreme Court rejected the gun lobby's argument that the initiative was too broad and the language misleading.
Robyn Anderson, who provided the killers three of the guns used at Columbine, bought them at a Denver-area gun show. Anderson, who was 18 when she bought the guns, testified before the Colorado Legislature that she would not have bought the weapons if she had to go through a background check.
Teen-agers Eric Harris and Dylan Klebold killed 12 students and a teacher before killing themselves in the April 20, 1999 massacre.
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