But, so far, President Donald Trump's administration has continued to insist that the North cannot be permitted to deploy its missiles and has vowed to ramp up economic sanctions still further.
"We have a long list of additional potential sanctions, some of which involve potential financial institutions," Secretary of State Rex Tillerson said, insisting the pressure strategy remains viable.
"As a diplomat, we keep working on it every day," he said.
Tillerson has been the main US champion of a diplomatic resolution to the crisis, hoping that economic and diplomatic isolation will force Kim to agree to talks to negotiate his disarmament.
The diplomatic route has borne fruit: Several countries have cut relations with the North, the UN Security Council has approved tougher sanctions and China has promised to enforce them.
But Kim has not blinked. He continues to trade public insults and threats of war with Trump, and on Tuesday he defiantly tested a powerful intercontinental missile in defiance.
In short, as Tillerson's spokeswoman Heather Nauert said on Wednesday, "North Korea is showing no interest in sitting down and having conversations with the world at this point."
Privately, however, some US diplomats admit Kim has already got what he wants, a credible nuclear deterrent, and many independent observers say Washington will just have to live with it.
"The North Koreans have always been willing to talk, they're just not willing to talk about giving up their nuclear weapons," argues non-proliferation expert Jeffrey Lewis of the Middlebury Institute.
"Having got this far they're not going to talk about that," he said "We can talk about deterrence, stability, reducing tensions, resolving security issues, about living with a nuclear North Korea."
Washington is not yet ready to do this. In the aftermath of Tuesday's test Trump and Tillerson hit their phones to reassure allies of their resolve and press China for greater efforts.
The United States will urge the UN Security Council to further increase international sanctions and is considering calling for an oil embargo and inspections of shipping headed for North Korea.
As Abraham Denmark, director of the Asia program at the Kissinger Institute, wrote on Twitter: "US still has a lot of options to respond to the ICBM test: Oil embargo, maritime interdiction, ban on foreign labor, secondary sanctions, deepen diplomatic isolation, strengthen military posture in region.
"Will these bring complete, verifiable, and irreversible dismantlement of the DPRK's nuclear program? Doubtful," he wrote.
"If Pyongyang truly believes it has completed developing and demonstrating a credible nuclear deterrent, this may be an opening for diplomacy."
China, the North's giant neighbor and main trading partner, is reluctant to take any measures that would destabilize the regime and lead to chaos, refugees or a US occupation force on its border.
And in any case, it is far from clear that sanctions could ever convince Kim -- who has made a strategic decision that only nuclear weapons can protect his rule and win his regime respect.
As Lewis explains, years of sanctions have failed to prevent Pyongyang from developing bombs and missiles, and they won't change the mind of a leader who fears a grisly fate if overthrown.
"The thing the North Koreans are afraid of is ending up like Saddam or Kadhafi -- and there are no sanctions in the world that are worse than that!" he told AFP.
If sanctions won't work, and Washington is not prepared to admit that Kim has won his bet on becoming a nuclear power, then might Trump make good on his threat to rain "fire and fury" on his foe?
The option remains on the table, and the United States continues to train with South Korea forces despite calls from China and others for a freeze on exercises as a gesture of reassurance.
But privately, US officials and diplomats in Washington admit that the options for confronting a nuclear-armed North Korea are limited, with any strike likely to trigger a war that could leave millions dead.