(CNN) -- Sen. John McCain said Sunday that he opposes the thought of filibustering a debate over gun legislation that will probably be brought to the Senate floor this week, despite threats of such action by fellow Republican senators.

"I don't understand it. The purpose of the United States Senate is to debate and to vote and to let the people know where we stand," Arizona's McCain said on CBS' "Face the Nation."

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 to be sent Monday to Senate Majority Leader Harry Reid, they wrote that 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."

The additional names include Sen. Marco Rubio, R-Florida; Sen. James Inhofe, R-Oklahoma; Sen. Jerry Moran, R-Kansas; Sen. Richard Burr, R-North Carolina, Sen. Ron Johnson, R-Wisconsin; Sen. Mike Enzi, R-Wyoming; Sen. James Risch, R-Idaho; Sen. Mike Crapo, R-Idaho, Sen. Dan Coats, R-Indiana, and Sen. Pat Roberts, R-Kansas.

The three-paragraph letter doesn't include the word "filibuster" but appears to be a warning that the Republican will vehemently stand against any "vehicle for any additional gun restrictions."

McCain, who also criticized Paul's filibuster last month over the administration's drone policy, said Sunday that he would not encourage such an approach.

"I don't understand it," he said. "What are we afraid of?"

Although recent polls show that an overwhelming majority of Americans favor an expansion of the background check system to include private transactions, such as those made at gun shows, sharp division over the issue is expected in the Senate.

The upper chamber is on schedule to begin voting on gun control measures as soon as this week, when Congress returns from its spring break, but Democratic sources admit that the gun bill as currently written does not have the 60 votes needed to break a filibuster.

The powerful National Rifle Association is staunchly opposed to the bill. It favors expanding the system to include more data on those with a history of mental health issues but fears that a broader expansion or records of sales could violate Second Amendment rights and lead to further restrictions.

Republican Sen. Tom Coburn of Oklahoma is shaping up to be an influential figure on the bill's trajectory, as he strongly opposes a point in the legislation on keeping records on gun owners.

Meanwhile, the White House has been ratcheting up its own pressure on Congress to pass the legislation. President Obama urged action last week when he traveled to Colorado, site of a movie theater massacre in July. On Monday, Obama will make a visit to Hartford, Connecticut, not far from the Newtown elementary school where 20 children and six adults were killed nearly four months ago.

"On the eve of Senate consideration of gun safety proposals the President will speak, as he did at the State of the Union, about the obligations the nation has to children lost in Newtown and other victims of gun violence to act on these proposals," a White House official said.

McCain said Sunday that his decision on whether to support the bill coming to the Senate would hang on a multitude of questions, indicating further the need for debate.

"It depends on how they're carried out, how long, what the depth of it is," he said of the background checks. "This is another reason why we need to go to the floor. Everybody wants the same goal, and that is to keep the guns out of the hands of criminals and people who are mentally disabled. And background checks are being conducted. Are they sufficient? Are there ways we can improve those? Then I think that's a subject the American people and the Congress could be helped by if we have a vigorous discussion."

CNN's Dana Bash, Ted Barrett and Jessica Yellin contributed to this report.

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