More than 190 nations agreed to the accord in December 2015 in Paris, and 147 have since formally ratified or otherwise joined it, including the US - representing more than 80 per cent of the world's greenhouse gas emissions.
A US withdrawal would remove the world's second-largest emitter and nearly 18 per cent of the globe's present-day emissions from the agreement, presenting a severe challenge to its structure and raising questions about whether it would weaken the commitments of other nations.
Trump has already, through Executive Orders, moved to roll back key Obama Administration policies, notably the EPA's Clean Power Plan, that comprised a key part of the US's Paris promise to reduce its emissions 26 per cent to 28 per cent below their 2005 levels by 2025.
As of 2015, emissions were 12 per cent lower, according to the US Energy Information Administration.
The Paris decision has deeply divided the Administration, with internationalists, such as Tillerson, arguing that it would be beneficial to the United States to remain part of negotiations and international meetings surrounding the agreement, as a matter of leverage and influence.
Conservatives, such as Pruitt, have argued that the agreement is not fair to the United States and that staying in it would be used as a legal weapon by environmental groups seeking to fight Trump environmental policies.
As a result of Trump's environmental policies, it has been clear that it would be impossible to honour the Obama Administration's Paris pledge.
That leaves Trump with two clear choices: withdraw from Paris or revise the US pledge downward to something more realistic in light of domestic policies, but nonetheless stay in the accord.
A downward revision would certainly prompt criticism from the international community, but not nearly so much as an abandonment. The Paris agreement is, after all, the first global accord on climate change action that has managed to unify both developed and developing nations behind a single framework to cut emissions.
Moreover, the accord is flexible in the sense that it does not mandate that any nation achieve any particular level of emissions cuts. Rather, every nation under the agreement pledges to do the best it can, and to participate in a process in which nations will regularly increase their ambitions over time.
Already, reports that Trump could withdraw the US from the agreement were causing waves today. Elon Musk, the CEO of Tesla, tweeted that if Trump does leave the accord, he would have "no choice but to depart councils" on which he has advised the President in the past. (Musk has been part of Trump's White House manufacturing jobs initiative.)
The ultimate goal of the Paris agreement is to hold the warming of the planet to "well below" two degrees Celsius of warming above the temperatures found in the preindustrial times of the late 1800s. The Earth is already about 1C warmer than it was at that time, scientists have determined, and current and near future emissions seem quite likely to take the planet past 1.5C in the coming decades.
Recent research has highlighted that above 2 degrees, major threats could ensue for Earth systems ranging from coral reefs to the planet's vast ice sheets.
According to the agreement, a party that has fully joined the accord, as the United States has, cannot formally withdraw for three years after the date of joining - and that is then capped by an extra year-long waiting period.
If this language frustrates Trump enough, he could opt to withdraw from the more foundational UN Framework Convention on Climate Change, which laid the groundwork for the Paris deal and was signed by President George H.W. Bush and ratified by the Senate in the early 1990s.
But that is an even more radical move, which would further withdraw the United States from all international climate change negotiations.
The back-and-forth in the Trump Administration over whether to stay part of the Paris agreement has triggered an outpouring of opinion and lobbying, perhaps most of all from corporate America, which has strongly supported the accord. Companies ranging from Apple to ExxonMobil have endorsed advertisements or statements supporting the accord, saying it won't harm the competitiveness of US business.
In light of this, it will be difficult for the President to argue that the Paris agreement hurts the US economy. The agreement's flexibility also means that it does not impose any specific requirement to cut emissions by a particular amount.
Because the United States is the second-largest emitter, removing the country from Paris could also remove 21 per cent of the emissions reductions that would have been achieved by 2030, according to an analysis by the think tank Climate Interactive. Other countries would have to make up the difference, with the likeliest candidates being China - the world's top emitter - or India, a nation expected to experience some of the fastest emissions growth in coming decades.
