That vision is to strike a wide-ranging deal that would limit the arsenals of not only the US and Russia, but also China for the first time.
And as the talks were taking place in Geneva, the clock continued to run down on the last remaining major nuclear deal between the US and Russia, which control 90% of the world's nuclear warheads.
If the New Start deal is scrapped, experts fear a return to a world without limits on nuclear stockpiles. The US and Russia could quickly ramp up the number of warheads deployed on sea and on land. With their nuclear ambitions unchecked, it would be almost impossible to convince other nations, like China, to exercise restraint.
In the absence of transparency, experts said, worst-case scenario thinking could contribute to an even more hostile geopolitical landscape. With global powers on tenterhooks, the risk of a miscalculation -- and a knee-jerk deployment of a nuclear weapon -- would increase.
"This would be the first time since 1972 that the US and Russia, previously the Soviet Union, would not have limits on their arsenals. It would make an already difficult and dangerous relationship all the more difficult to manage, and could cause one or the other side to accelerate their nuclear stockpiles," Daryl Kimball, director of the Arms Control Association, told CNN.
"It would be a world that we have not seen in a long time."
'A poison pill'
In January, Trump announced his intention to seek a new nuclear treaty and offered a vision of what would come next if he couldn't strike a deal.
But by all accounts, 19 months is not enough time to negotiate a brand-new agreement -- even if China was on board, which it is not.
"We oppose any country's attempt to make an issue out of China on arms control and will not participate in any negotiation for a trilateral nuclear disarmament agreement," Chinese Foreign Ministry spokesman Geng Shuang said during a press briefing in May.
"This proposal for a trilateral agreement is, in reality, a poison pill designed to provide a pretext to allow for the [New Start] treaty to expire," Kimball told CNN.
President Vladimir Putin, who has suggested Russia would be open to renewing the New Start treaty, has warned that letting the pact lapse could risk an arms race.
The ditching of nuclear treaties by the Trump administration has already contributed to the weakening of norms, and casts other multilateral agreements, like the Nuclear Nonproliferation Treaty (NPT) into doubt, experts said.
Under the NPT, one of the world's most important foundational nuclear treaties, nuclear-weapon states -- the US, Russia, China, France and the UK -- commit to ending the arms race and achieving nuclear disarmament, while non-nuclear-weapons states agree to forgo developing or seeking nuclear weapons.
But if the US and Russia abandon an agreement designed to reduce their nuclear stockpiles, it will become far more difficult to make non-nuclear states stick to their commitments, according to Tytti Erästö, a researcher for the SIPRI Nuclear Disarmament, Arms Control and Nonproliferation Programme.
"Without these treaties you can't even speak about violations or limits -- basically anything is allowed," Erästö told CNN.
"For new potential proliferators, the weakening of international norms and the legitimacy crisis within the Nuclear Nonproliferation Treaty may remove some of the normative restraints to developing nuclear weapons. I don't think any country would go develop a nuclear weapon just because of this, but it may impact decisions in the future about whether or not to acquire them."
One eye on China
China is steadily building and modernizing its arsenal, according to Zhao Tong, a fellow at the Carnegie-Tsinghua Center for Global Policy in Beijing.
"It's a trend that makes the US increasingly worried," Zhao told CNN.
Zhao warned that a collapse of the New Start treaty would pose significant implications for Chinese nuclear thinking.
"The Chinese embrace deep distrust against the US, and against Russia to some extent, even under current conditions," Zhao said. "So you imagine if there is no formal agreement, no verification letters, how Chinese experts would trust the unilaterally declared amounts. It is very easy for the Chinese expert community to develop exaggerated threat perceptions."
And that fear would ultimately drive further growth of the Chinese nuclear arsenal.
Arms control agreements supply parties with a basic sense of certainty about each other's capabilities. They help mitigate misunderstandings among big powers, build transparency measures through mutual verification and contribute to confidence building -- cultivating a habit of cooperation through open channels.
Without them, the effect is a much more uncertain world with fewer rules regulating the world's most dangerous weapon.
The possibility of the New Start treaty's demise offers a window into the atmosphere that could exist without any nuclear limits at all.
"If there is no arms control, opportunities of substantive exchange would be lost and the nuclear communities would stop talking," Zhao said.
"In that environment I'm afraid the appreciation and spirit of cooperative security would be lost."