(CNN) - The Republican Party appears split over whether to block gun legislation in the Senate.
While more than a dozen GOP senators have stated they plan to block the proposed bill from proceeding, a number of Republicans are saying the public deserves to hear debate over the legislation. Senate Minority Leader Mitch McConnell has also vowed to oppose the bill as it now stands.
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Both senators from Georgia, Sen. Johnny Isakson and Sen. Saxby Chambliss said Tuesday they won't join those in their party who may stall the bill.
"I don't think I'm going to support that," Chambliss told the Chattanooga Times Free Press. "I just don't think it's the right thing to do."
"I think it deserves a vote up or down," Isakson said on CBS.
On Tuesday, Senate Majority Leader Harry Reid said a vote on whether to open debate on the bill come Thursday. Reid needs 60 votes to begin consideration and prevent a filibuster.
There are 55 Democrats in the Senate (including two independents who caucus with the party) and 45 Republicans, meaning if all Senate Democrats vote to proceed, Reid will need at least five Republicans to do so, as well.
Though he's not in the Senate, Rep. Peter King of New York took a similar stance, saying Tuesday the upper chamber should allow a vote to go through.
"The American people are entitled to a debate. And to me, to use Senate rules to block a debate on an issue of this importance is just wrong," King said on CNN's "Starting Point."
At issue is a bill that includes calling for a universal background check system.
However, CNN reported that recent talks in the Senate indicate the system may be expanded to include purchases at gun shows and online, but would not be universal in covering private sales between individuals, as backed by President Barack Obama and many Democrats.
A trio of first-term GOP senators - Rand Paul of Kentucky, Mike Lee of Utah and Ted Cruz of Texas - stated in a letter last month that they will block any gun control legislation that they consider a threat to Second Amendment rights.
Several other Republican senators joined in, and in an expanded letter sent Monday to Senate Majority Leader Harry Reid, they wrote they would oppose a bill that "would infringe on the American people's constitutional right to bear arms, or on their ability to exercise this right without being subjected to government surveillance."
Sen. John McCain questioned why some in his party were trying to stand in the way of a vote. "I don't understand it," he said Sunday on CBS. "What are we afraid of?"
Former New York City Mayor Rudy Giuliani agreed with McCain, saying Monday on CNN's "Piers Morgan Live" there's no point for Republicans to try to obstruct the bill, when it's almost certain the bill will fail in the GOP-controlled House.
"(The Senate) should vote up or down on this," he said. "I don't understand why the Republican Party is creating this problem for themselves about filibustering. If they want to block this legislation, they have a House of Representatives in which to do it. I don't know why they're creating this sort of additional political issue that isn't required."
Recent polls show an overwhelming majority of Americans favor making a change to the background check system – a fact President Barack Obama raised Monday in his speech near Newtown, Connecticut.
"If our democracy's working the way it's supposed to, and 90% agree on something, in the wake of a tragedy, you would think this would not be a heavy lift," Obama said, saying the Republicans who were vowing the filibuster the bill were, in essence, telling Americans that their "opinion doesn't matter."
This week, CNN TV and CNN.com will take an in-depth look at “Guns Under Fire: A CNN Special Report On Background Checks.” On Tuesday night at 8 p.m., AC360 will debut an exclusive interview with former Rep. Gabrielle Giffords, who was shot in the head two years ago in Arizona. On Wednesday, the network will look at gun control and background checks as Congress is expected to tackle the issue head-on in the coming days. Watch CNN TV and follow online at CNN.com or via CNN's apps for iPhone, iPad and Android.