While Chinese apparatchiks will, presumably unquestioningly, jump to realize President Xi Jinping’s order to reduce carbon emissions in an ambitious deal with the United States, Barack Obama will come home to a newly elected Congress that will probably tell him to neuter his climate change agenda or be prepared for the kind of knock-down, drag-out fight that could potentially end with a government shutdown.

Republicans, led by presumptive new Senate majority leader, Mitch McConnell, of coal-loving Kentucky, have already criticized the Beijing agreement.

But what can McConnell and the GOP really do to stop it? The deal is not a formal treaty, so Obama will not need the Senate to approve it. And while Republicans could pass bills to block provisions of the deal from going into effect, doing so would probably not be much more than symbolic, since Obama can simply click his veto pen into action. The constitution requires two-thirds of the Senate and House to vote to override a veto, and despite their recent wins, the GOP still doesn’t have those kinds of majorities.

But while Obama and the executive branch agencies that he controls, like the Environmental Protection Agency (EPA), can act on their own to implement the agreement, under the US constitution’s system of checks and balances, Congress pulls the pursestrings. When the next bill containing the EPA’s budget – or the next omnibus piece of legislation to keep the entire government running – comes round, Republicans can attach provisions called “riders” that would undermine, defund and restrict parts of the climate plan. Clinging to an unrelated bill like legislative barnacles, riders could, for example, prevent the EPA from using any money to actually enforce the rules and regulations necessary to implement the agreement.

Riders on an omnibus budget could also put the president in a pickle: unless Obama signs legislation to cripple his own major accomplishment, he could risk shutting down the government. That could flip the circumstances of the 2013 government shutdown, making Obama look like the villain who refuses to keep the government going, and turning Republicans into the reasonable lawmakers who “get us out of government shutdowns”, as McConnell put it.

Republicans could also try to bargain with the president, using narrowly written bills as leverage, getting victories of their own while perhaps conceding something to Democrats in exchange. Obama has never spoken out particularly strongly against the Keystone XL pipeline, for instance, and both parties could try to use it as a bargaining chip.

The GOP could also simply try to clog the works a bit. Senator Jim Inhofe, the author of The Greatest Hoax: How the Global Warming Conspiracy Threatens Your Future, would have some power to do that as chair of the environmental committee. Inhofe will likely launch investigations, hindering and possibly delaying implementation of the agreement with hearings and squads of investigators. Green energy projects will be examined with a microscope; green investments decried. Zones of EPA jurisdiction, as tiny as a stream or strait or islet, will be argued and bickered about, and officials in the EPA will have their lives made miserable as senators try to cow them with pressure.

Inhofe can also contest EPA rulings like the “endangerment finding”, under which the agency declared that greenhouse gases were a danger to public health and merited regulation. Reports by Inhofe’s investigators can then be used by businesses who challenge the EPA in court, sending the “war on coal and oil” into the long and expensive trenches of the judicial system.

And like most political agendas, there’s always the next election to consider: if the GOP can handcuff the EPA as long as possible, they may be able to play the electoral field into a 2016 win, getting a less-green president in office and shutting the whole thing down.