While many cheered the White House's plan to cut carbon emissions from power plants last month, there was one group of potential supporters that was not happy: nuclear power advocates.

After a long debate over how to credit nuclear plants for their zero-carbon electricity, the Environmental Protection Agency will not allow the country's existing fleet to qualify under its final plan.

In a welcome change from the draft rule, the five nuclear plants currently under construction will qualify as part of state plans to cut carbon emissions. But nuclear proponents are upset that the country's largest provider of emissions-free power is getting left out.

It also has some worried about the viability of Obama's marquee climate plan.

Without a federal strategy for keeping America's 105 gigawatts of nuclear reactors running for the next couple of decades, emissions goals under the Clean Power Plan will be "extremely difficult if not impossible," concludes a new report from Third Way, a centrist think tank based in Washington, D.C.

The Clean Power Plan was crafted to help lower U.S. carbon emissions from existing power plants by 32 percent from 2005 levels. It was written to maximize flexibility for states, which can choose any mix of low- to no-emission options to meet their specific targets. But they won't be able to use their existing nukes.

In partnership with MIT researchers, analysts at Third Way modeled what would happen if nuclear plants started closing in large numbers. The results were not promising.

"Emissions increases due to nuclear retirements would sabotage the carbon reductions targeted by the EPA’s Clean Power Plan and, in the worst case, could wipe out a decade’s worth of progress by effectively returning U.S. electricity sector emissions to 2005 levels," concludes the report.

The researchers created three scenarios. Under the optimistic case, all 100 reactors around the country get license renewals until 2035 -- two decades longer than their 40-year operating licenses. Under a middle case, no licenses are extended and more than half of reactors shut down. And under a (very unlikely) worst-case scenario, America decides to shut down all nuclear plants aside from the handful being built right now.

Even under the middle scenario -- a likely one -- America's carbon emissions in 2035 would be well above the targets set by the Clean Power Plan. That's because the MIT model shows that most retired capacity will get filled in by natural gas, not renewables.

"As these results indicate, any widespread retirement of America’s nuclear power plants would make it extremely difficult if not impossible for the Clean Power Plan to reach its emissions targets of 32% below 2005 levels. Preserving America’s nuclear fleet is essential to the nation’s carbon reduction goals," write the researchers.

Shutting down nukes could also make renewables less valuable under the plan because they'll be used to fill in the zero-emissions gap. "Replacing nuclear with renewables is like running to stay in one place," they wrote.

Jesse Jenkins, a consultant on the report, explained the conundrum in a companion piece at the Energy Collective: "To simultaneously displace coal and gas and replace the fifth of U.S. electricity supplied by carbon-free nuclear, renewables (excluding hydropower) would need to collectively supply about 31 percent of U.S. electricity by 2030, a nearly 4.5-fold expansion."

There are a few caveats to the analysis, however.

Nuclear power's struggles go well beyond licensing. Cheap natural gas, competitive renewables and stagnating demand are destroying the profitability of nuclear plants. Even if facilities were allowed to operate for a couple extra decades, that doesn't mean they would be able to compete in the market. Given the cost trajectory forsolar wind and batteries, it's hard to imagine that operating existing nuclear plants gets any easier in the coming decades. The Third Way analysis does not go into much detail on this point.

The model also shows that renewables will not be able to make up for the decline in nuclear electricity. However, the study only looks at renewables supported by existing state-level mandates. Under the Clean Power Plan, more states will likely set targets. More importantly, corporations, cities and utilities are now consistently purchasing renewable electricity outside of any mandates because it's the cheapest option.

It's hard to know exactly what renewables growth will look like 20 years from now. But relying only on a business-as-usual framework doesn't tell us much about how the market will grow by 2035.

Although the analysis has a few modest limitations, it does demonstrate the fragility of the Clean Power Plan. If nuclear plants continue to drop offline (and renewables lose their federal tax credits at the same time), America may find it difficult to achieve the carbon reduction targets that seem so doable today.

"We must understand the contribution the U.S. civilian nuclear fleet has had on keeping emissions down and the devastating consequences we would face if this energy source were to gradually fade away, let alone rapidly disappear. The Clean Power Plan has paved the way for emissions reductions in the United States power sector. Shutting down nuclear power plants is a surefire way to undermine these goals," concludes the report.

How ambitious is Obama's climate plan? Listen to the interview with Politico's Michael Grunwald on The Energy Gang for context: