Washington (CNN) President Donald Trump's escalated statements against North Korea have revived questions in Washington about the President's authority to approve the use of nuclear weapons.

One senator, Democrat Ed Markey of Massachusetts, said Trump's rhetoric "borders on presidential malpractice," and he's calling attention to legislation he drafted that would require congressional approval before any President could sign off on a first-use nuclear strike.

"The 'cooler heads' and 'strategic doctrine' that once served as our last, best hope against the unthinkable seem less reassuring with every tweet President Trump sends," Markey said in a statement.

His concern comes after Trump -- while responding to remarks from North Korean leader Kim Jong Un -- tweeted a comment Tuesday that quickly fueled speculation of potential nuclear war.

"North Korean Leader Kim Jong Un just stated that the 'Nuclear Button is on his desk at all times.' Will someone from his depleted and food starved regime please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!" Trump tweeted

North Korean Leader Kim Jong Un just stated that the "Nuclear Button is on his desk at all times." Will someone from his depleted and food starved regime please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works! — Donald J. Trump (@realDonaldTrump) January 3, 2018

Kim said Monday in his annual New Year's Day address that "the entire mainland of the US is within the range of our nuclear weapons and the nuclear button is always on the desk of my office. They should accurately be aware that this is not a threat but a reality."

Sanctions and "other" pressures are beginning to have a big impact on North Korea. Soldiers are dangerously fleeing to South Korea. Rocket man now wants to talk to South Korea for first time. Perhaps that is good news, perhaps not - we will see! — Donald J. Trump (@realDonaldTrump) January 2, 2018

Markey's bill currently has 12 Democratic co-sponsors, but Sen. Bob Corker, a Tennessee Republican who's the chairman of the Foreign Relations Committee, said Wednesday there were no plans to bring up a bill that changes the President's authority. Still, Markey intends to make a renewed push for additional co-sponsors now that the Senate is back from its winter break. Rep. Ted Lieu, a Democrat from California, sponsors the companion bill in the House.

"The question is how long will it take, how many of (Trump's) statements will it take before the Republican leadership is willing to actually have a debate about this issue," Markey told CNN.

Washington reacts

Sen. Ben Cardin of Maryland, the top Democrat on the Foreign Relations Committee, said Wednesday on CNN that "the President's tweets have made it more difficult for diplomacy to work."

Former Director of National Intelligence James Clapper, who served in the Obama administration, said Tuesday night that he's worried the US is "probably closer" to a military encounter with North Korea "than we have been for some time" because of Trump's recent tweets. "It's almost as though he's taunting him to press the nuclear button, saying, hey, mine works, by the way," he said on CNN.

Sen. John Cornyn, the No. 3 Republican in the Senate, also expressed some concern.

"It's a very serious issue, and I don't know how anybody's interests are served by escalating that rhetoric," the Texas senator told reporters Wednesday. "I do think it's really important to try and come up with a diplomatic solution, and I applaud Secretary (of State Rex) Tillerson and the administration for trying to do that and getting China more engaged."

Sen. Lindsey Graham, a South Carolina Republican, said he wasn't sure the tweet was "the right approach." Sen. Rob Portman, a GOP Ohioan, said the tweet was "not my style" but argued that tougher sanctions on North Korea are "starting to bear fruit."

Many Republicans largely downplayed the tweets. Others simply avoided the topic. Corker, who previously said Trump was setting the country on a path to World War III , was asked at least seven times by reporters in the halls of Congress. He declined to comment.

Some lawmakers appeared to appreciate Trump's tough-talking rhetoric.

"We finally have a president who is actually dealing with the problem at hand instead of what we've seen previously, which is ignoring the problem," said Republican Sen. John Barrasso of Wyoming.

White House spokeswoman Sarah Sanders on Wednesday defended Trump's tweets, telling reporters that "this is a president who is not going to cower down, is not going to be weak."

President's power in the spotlight

The President's authority over nuclear weapons has been a hot topic in the past year as tensions between the United States and North Korea have worsened and as Trump has made provocative statements designed to intimidate.

The Republican-led Senate Foreign Relations Committee held a hearing in November examining the system that's in place to order a nuclear strike. Officials argued there are multiple steps in place to ensure that any decision is thoroughly reviewed beforehand. Trump himself has had multiple briefings on the nuclear launch cycle and more conventional, non-nuclear alternatives.

"I think that we have to keep trust, keep faith in the system that we have, that has proven effective now for decades," said Defense Secretary James Mattis.

Dr. Peter Feaver, a professor of public policy and political science at Duke University, also explained that the process is not as simple as pressing a button . "The President by himself cannot press a button and cause missiles to fly. He can only give an authenticated order which others would follow and then missiles would fly," Feaver said.

Brian McKeon, who served as principal deputy undersecretary of defense for policy during the Obama administration, also warned against changing the laws.

"I think hard cases make bad law, and I think if we were to change the decision-making process in some way because of a distrust of this President, I think that would be an unfortunate precedent," he said at the November hearing.

Corker said Wednesday that the hearing was "educational" but there's no effort underway to consider legislation.

"I don't think there's any contemplation of any changes, but the hearing was great from the standpoint of people being aware of how the whole process works," he said.