(CNN) Congress is considering a more aggressive approach toward China as it struggles with North Korea's nuclear weapons and missile advances.
Since Congress passed a new round of sanctions against Pyongyang in July, North Korea conducted its second intercontinental ballistic missile (ICBM) test and sixth nuclear test -- the latest believed to be a hydrogen bomb -- and made advances toward miniaturizing a nuclear weapon.
There's broad agreement on Capitol Hill and in the Trump administration that China is key to a diplomatic answer to the North Korean crisis, but getting China to play ball has long proved to be problematic.
Some lawmakers say they should consider fresh sanctions targeting China to convince Beijing to do more, but there are concerns that going after China will also harm the US -- and it may not sway Kim Jong Un anyway.
"Economic sanctions against China sounds great, but those will have an impact on the United States," said Virginia Rep. Rob Wittman, a senior Republican on the House armed services committee. "People have to be willing to say if we're going to do that, there's going to be some suffering here. So we have to be willing, if we're going to do that, to be all in, which makes it more of a challenge to convince folks here it needs to happen."
California Rep. Ed Royce, the chairman of the House foreign affairs committee, told CNN Tuesday that he's pressing the administration to put more economic pressure on North Korea.
House Republicans added the House's North Korea sanctions bill to the sanctions package including Russia and Iran that President Donald Trump signed into law last month, which tightened sanctions on foreign companies doing business with North Korea.
While Royce didn't mention China specifically, he said he now wants the administration to use the full weight of the new law for broader sanctions that would impact Beijing's trade with Pyongyang.
"I think we can cut off the shipping, access to the ports, the sanctions on the entire financial system," Royce said. "It's always been done in fits and starts, it's never been done in consistent relentless way in which you shut down the billions of dollars they need in hard currency."
US Ambassador to the United Nations Nikki Haley said Monday that the US is preparing a new Security Council resolution to punish North Korea for its latest nuclear test.
Meanwhile, the President's national security team, including Defense Secretary James Mattis and Secretary of State Rex Tillerson, is briefing the full House and Senate Tuesday on the North Korean situation.
Democrats say they have faith in Trump's national security team, but they worry that the President's tweets -- from criticizing South Korea's approach to the North to suggesting the US could cut off all trade with China -- raise troubling questions about the administration's approach.
"I want to better understand how seriously I should take the tweets," Hawaii Democratic Sen. Brian Schatz told CNN. "I want to personally get clear on what American policy is. When we get briefed, I am reassured that there are rational sane people working a strategy."
At the same time, some lawmakers are skeptical that China really can take action to stop North Korea's nuclear ambitions, because China wants to avoid creating a failed state in the North.
"China can cut off all their energy tomorrow and North Korea would be on their knees," said Washington Rep. Adam Smith, the top Democrat on the House armed services committee.
"But I don't think North Korea's response would be to stop building missiles and stop building nuclear weapons. Their response would likely be to attack, or the regime would be thrown into chaos, and China doesn't want that."
Congress is also looking at more immediate ways to bolster the defenses of South Korea and US territories from a potential North Korean missile attack.
In addition to boosting the Pentagon's budget for missile defense and nuclear modernization, Congress has largely endorsed selling additional weapons to South Korea -- which the White House touted in a readout of Trump's conversations with South Korean President Moon Jae-in.
"We need an all-hands push to make sure that China feels the pain of this and is engaged in putting more economic pressure on North Korea, and frankly, to escalate the preparations for our vital allies in the region to make sure that South Korea and Japan have the anti-missile defenses they are seeking," Delaware Democratic Sen. Chris Coons told CNN's Erin Burnett.
South Korea this week approved the installation of four additional launchers of the US-made Terminal High Altitude Area Defense (THAAD) missile defense system. THAAD is a sore spot for China, which considers the system a threat in the region, though the US insists its purely to guard against the North Korean missile threat.
China and Russia have proposed a so-called "freeze-for-freeze" plan for North Korea to suspend its missile program in exchange for the US and South Korea to stop joint military exercises. But the US has rejected the notion -- Haley called it "insulting" on Monday to suggest that the US and its allies would lower their guard.
But Sen. Ed Markey, a Massachusetts Democrat, suggested that some kind of concession to China would be needed in order for Beijing to get North Korea to the negotiating table in a legitimate fashion.
"If we want the cooperation of the Chinese on the issue of this 22% increase in trade between China and North Korea over the last year, in cutting off the oil to North Korea, and giving China assurances that our goal is not to decapitate the North Korean regime but just end the ballistic missile and nuclear weapons program -- then we are going to have to give to China, some of the concessions which are going to be sincere in order to wind up with them as our partner in helping to isolate the North Koreans," Markey said on CNN's "New Day."
This story has been updated.