Katowice, Poland (CNN) The UN climate talks in Poland -- an attempt to save the world from disastrous levels of global warming -- are sputtering toward a conclusion after two weeks of discord.

"They're going nowhere -- for Tuvalu, for small counties," Prime Minister Enele Sopoaga of Tuvalu, an island country in the Pacific, said Friday morning. "What we have on the table is very disappointing, very frustrating. We are unhappy. We are going back on the Paris Agreement -- what we agreed to three years ago. It looks like people still do not trust each other. There is a lack of confidence [and] trust on the principles of working together."

Sopoaga said the United States alone is standing in the way of agreement.

"It's the White House alone that's dragging their feet," he said. "Our country is already going underneath the water. I hope the White House reconsiders its position."

At issue for countries like Tuvalu, which are feeling the effects of climate change but doing little to cause it, is debate about whether to "welcome" a recent report from the UN Intergovernmental Panel on Climate Change that says pollution from fossil fuels and other sources must be cut dramatically in just 12 years to avoid disastrous warming.

Last weekend at the 24th Conference of the Parties to the United Nations Framework Convention on Climate Change, the United States, Saudi Arabia, Russia and Kuwait declined to "welcome" that report, instead wanting only to "note" its existence, which is light-years away in diplomat speak. That disagreement, along with events at COP24 that promoted fossil fuel technologies, have cast a cloud over these negotiations, which are being held in Polish coal country.

Wider shot so you can get a sense of how much media interest these kids are drawing. Inspired by Swedish 15 yr old. Calling for global school walk out. Critical moment in the fight against fossil fuels and climate change. #COP24 #ClimateStrike pic.twitter.com/8GuUmCueEZ — John D. Sutter (@jdsutter) December 14, 2018

US President Donald Trump has pledged to pull out of the Paris Agreement. That can't technically happen until 2020, though, so the nation still has a presence in these talks.

Not everyone here sees the US playing the spoiler role in Poland.

"When Trump announced that the US would pull out of the Paris Agreement, we thought it would be reflected strongly in having a US administration blocking negotiations," said Manuel Pulgar-Vidal, president of a previous round of these negotiations, COP20, and global lead for climate and energy issues at World Wide Fund for Nature, a US-based environmental group.

"Fortunately, that hasn't happened," he said. "The US negotiators and head of delegation have not been a strong supporter -- but haven't blocked negotiations."

The point of the negotiations is to come up with a "rulebook" that will make real the Paris Agreement on climate change, to which countries agreed at these talks in 2015.

New, but not final, drafts of those rules were released on Thursday night and will continue to be revised. The talks were supposed to end Friday but now appear to be headed into the weekend, according to several observers and negotiators involved in the discussions.

Among the issues ministers are debating are rules for reporting emissions; financing -- or even reparations of sorts -- for developing countries as they deal with the effects of climate change; and, importantly, the symbolic issue about "welcoming" the best international science.

Members of the Global Campaign to Demand Climate Justice protest ahead of the final session of the COP24 summit on climate change in Katowice, Poland.

The Paris Agreement calls for countries to limit warming to 1.5 degrees Celsius -- or at most 2 degrees -- above pre-industrial levels. It's a global "peer pressure" agreement that relies on nations submitting their own plans for cutting pollution and reporting on those efforts. There are no financial penalties, for example, if nations fail to meet their pledges.

Partly for those reasons, it's crucial that there are clear and strict rules that require countries to report how much progress they are or aren't making to reduce pollution, said Bill Hare, a climate scientist and director of Climate Analytics, a nonprofit research and policy group.

Aspects of the current rules are "weak," he said, but could change.

"This is still in play as far as I'm concerned," he said Friday afternoon.

"We have some real concerns about certain areas," said David Waskow, international climate director at the World Resources Institute, an environmental policy group. He identified the draft rules around emissions trading as one weakness. Another potential blocker in the ongoing negotiations "loss and damage": aid to poorer countries hurt by global warming.

There remains a sense of uncertainty in the air in Poland.

Until a final draft of the rulebook is available, it's hard to know how things will turn out, said Todd Stern, the United States climate envoy under the Obama administration.

"From what I've seen so far, it's edging its way toward a decent outcome -- I hope," Stern said, noting that most meetings are taking place behind closed doors.

"But we haven't seen a document yet. Big things can happen between documents."

Others are even more optimistic. Teresa Ribera, Spain's minister for ecological transition, is "sure" that an agreement will be reached in Poland, she said Friday afternoon. "There's nothing that could explain why there would not be an agreement here," she said.

The main hall of the sterile conference center in Poland where the talks are being held was filled twice on Friday with protesters demanding swifter action from world leaders. A group of Polish children, inspired by a teenager from Sweden, walked out of school this morning. On Twitter, Greta Thunberg, the Swedish teen, called for a global walkout for climate action.

"It's about time those with power and the resources come down to see what life is like with the people," said Taneti Maamau, president of Kiribati, another island nation in the Pacific Ocean. He was overlooking protests in the conference center on Friday afternoon. Environmentalists were chanting "keep it in the ground" as they held signs saying, "Which side are you on?" and "System change not climate change."

Countries like Tuvalu, which arguably have the most to lose if these talks derail, were on edge about the results of the rulemaking conference, which follows several alarming reports about the clear state of climate science and the fact that global pollution is still climbing.

"It's so unfortunate -- despite the warnings from the IPCC special report -- that we are stuck in our own self-interested agendas here in this process," Tuvalu's Sopoaga said of the UN report.

"We should rise beyond this," he said. "We cannot allow this to happen."