(CNN) – Monday's deadly school shooting in Nashville has sparked a familiar cycle of condolences and calls to action among lawmakers in Washington, but both sides of the aisle have been quick to concede that the recent violence is probably not enough to sway a divided Congress to move substantive gun control efforts forward.

After three children and three adults were killed in a shooting at a private Christian elementary school in Nashville on Monday, President Joe Biden asserted that he's done all he can do to address gun control and urged members on Capitol Hill to act. But the shooting, so far, has not compelled lawmakers in Washington – particularly Republican leadership and some members representing Tennessee – to push forward gun control, signaling no end to the impasse within the GOP-controlled House and nearly deadlocked Senate.

The Nashville incident was just among the latest in 130 mass shooting incidents so far this year, according to data from the national Gun Violence Archive.

White House officials are not currently planning a major push around gun safety reform in the wake of the deadly Nashville school shooting, three senior administration officials said. But Biden and White House officials will continue to urge Congress to act.

Biden on Tuesday told CNN's MJ Lee, "I can't do anything except plead with the Congress to act reasonably."

"I have done the full extent of my executive authority – to do on my own, anything about guns ...The Congress has to act. The majority of the American people think having assault weapons is bizarre, it's a crazy idea. They're against that. And so I think the Congress could be passing an assault weapon ban," he added.

Biden has taken more than 20 executive actions on guns since taking office, including regulating the use of "ghost guns" and sales of stabilizing braces that effectively turn pistols into rifles. He also signed a bipartisan bill in 2022 which expands background checks and provides federal funding for so-called "red flag laws" – although it failed to ban any weapons and fell far short of what Biden and his party had advocated for.

Political realities of gun reform in the divided Congress

White House officials have been sober about the political realities Democrats face with the current makeup of Congress, where Republicans in control of the House have rejected Biden's calls for an assault weapons ban. Even when both chambers of Congress were controlled by Democrats during the first two years of Biden's term, an assault weapon ban gained little traction, in part because of a 60-vote threshold necessary for passage.

Many Republicans in Congress, including those in positions of leadership and in the Tennessee delegation, have either been reluctant to use the deadly violence in Nashville as a potential springboard for reform or they've outright rejected calls for additional action on further regulating guns, arguing that there isn't an appetite for tougher restrictions.

On Tuesday, House Speaker Kevin McCarthy would not answer questions on whether any congressional action should be taken on guns after the shooting in Nashville. And House Majority Leader Steve Scalise, a Republican from Louisiana who survived being shot in 2017, demurred when asked if the most recent school shooting in Nashville would move Congress to address any sort of reforms.

"I really get angry when I see people try to politicize it for their own personal agenda, especially when we don't even know the facts," he said when asked if his conference was prepared to do anything to address the spate of mass shootings, mentioning only improving mental health and securing schools.

"Let's get the facts. And let's work to see if there's something that we can do to help secure schools," he added. "We've talked about things that we can do and it just seems like on the other side, all they want to do is take guns away from law abiding citizens. ... And that's not the answer, by the way."

Sen. Thom Tillis, a key GOP negotiator in last year's bipartisan gun legislation, said on Tuesday that he doesn't see a path forward on new gun legislation. Instead, he believes that lawmakers need to focus on implementing what has already been signed into law.

"The full implementation is going to take months and years," Tillis said of the gun bill that passed last summer. "There is a lot of unimplemented or to be implemented provisions in there. Let's talk about that first."

House Judiciary Chairman Jim Jordan, an Ohio Republican whose committee has jurisdiction over gun policy, said Tuesday that he doesn't think Congress should take action to limit assault weapons, though he declined to say why it's okay to ban fully automatic rifles but not semi-automatic weapons.

"The Second Amendment is the Second Amendment," he continued. "I believe in the Second Amendment and we shouldn't penalize law-abiding American citizens."

Sen. Lindsey Graham of South Carolina, the top Republican on the Senate Judiciary Committee, who has been involved in past negotiations on gun legislation, said: "I don't know if there's much space to do more, but I'll certainly look and see."

Graham said he is opposed to a ban on AR-15s -- which was one of the weapons the Nashville suspect used during Monday's shooting -- noting that he owns one himself and arguing that it would "be hard to implement a national red flag law."

Asked by CNN's Manu Raju why he wouldn't support a ban of AR-15s, Andy Ogles, who represents the district where Monday's shooting took place, replied, "Why not talk about the real issue facing the country -- and that's mental health." And Sen. Bill Hagerty, the Tennessee Republican, refused to discuss calls to ban AR-15s after the Nashville shooting.

"The tragedy that happened in my state was the result of a depraved person and somebody very very sick. And the result has been absolutely devastating for the people in my community. Right now with the victims, the family and the people in my community -- we are all mourning right now," Hagerty told CNN.

Asked about banning those weapons, he added: "I'm certain politics will wave into everything. But right now I'm not focused on the politics of the situation. I'm focused on the victims.

Tennessee GOP Rep. Tim Burchett told reporters that "laws don't work" to curb gun violence.

"We want to legislate evil -- it's just not gonna happen," he said. "If you think Washington is going to fix this problem, you're wrong. They're not going to fix this problem. They are the problem."

Asked by CNN why private citizens need AR-15s, Burchett pointed to self-defense. He also argued that even though other countries don't observe the United States' high frequency of shootings, "other countries don't have our freedom either ... And when people abuse that freedom, that's what happens."

Meanwhile, some Democrats in Congress are slamming House Republicans for their disinterest.

"As a country and as a Congress, we can do better and we know that, so shame on Speaker McCarthy for not bringing something up, for not announcing that we can and do more. All we're going to get are thoughts and prayers out of their Twitter accounts, and that's not enough" Democratic Caucus Chairman Pete Aguilar of California said during a press conference.

On the other side of the Capitol, however, Senate Majority Whip Dick Durbin told reporters that he is "not very hopeful" that the Senate can pass gun legislation this Congress.

"I'm not very hopeful, yet we have to try," he said.

Connecticut Democratic Sen. Richard Blumenthal called on Senate Majority Leader Chuck Schumer to force a vote on a semi-automatic weapons ban to put Republicans on the record.

"We need a fight in Congress, and I'm prepared to conduct that fight, others are as well," he told CNN. "And ultimately the American people deserve to know where each of us stands on common sense gun violence prevention."

Schumer would not say whether he intends to put legislation banning assault weapons on the Senate floor for a vote this Congress. There is nowhere close to enough support to overcome a legislative filibuster.

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