One possibility is using the appropriations process to block funds for implementing the deal, suggested Steve Bell, a former Senate Republican aide to the Budget Committee. "Other than just complaining about it, the only real thing they could do would be through appropriations," he said.
But even if Republicans win control of the Senate, the chances of getting such a measure signed into law are remote.
Still, Republicans, particularly House Republicans, might bring up a messaging bill explicitly prohibiting the president's pact, Bell added. They'd probably find support among pro-coal Democrats such as Rep. Nick Rahall of West Virginia, who knocked the "end-run around Congress."
Wednesday's attacks from Senate GOP leaders and candidates tracks with what is becoming a well-worn political dialogue between the GOP and the White House, one that stretches back at least as far as the president's pledge to use his pen and phone to go around GOP opposition in Congress.
The antipathy runs deep, with Republicans charging that the president refuses to work with them, and the White House lobbing the same charge in return. The result has been a legislative impasse, with the White House casting Republicans as obstructionists and the GOP billing the president as lawless.
Minority Leader Mitch McConnell, locked in a close reelection contest in Kentucky where he has linked his opponent to the president, panned the notion of avoiding Senate ratification, where a two-thirds vote is needed.
"Unfortunately, this would be just another of many examples of the Obama administration's tendency to abide by laws that it likes and to disregard laws it doesn't like—and to ignore the elected representatives of the people when they don't agree," he said in a statement.
The issue is playing out on the campaign trail in other contests, too. With Republicans in striking distance of taking the majority in November, GOP candidates in battleground states are seizing on the report.
Said Rep. Cory Gardner of Colorado, locked in a close race against Democratic Sen. Mark Udall: "Coloradans don't elect senators to watch them toss their power to the president, whether Republican or Democrat."
The Sierra Club, one of the groups that pushes for tough curbs on heat-trapping emissions, on Wednesday sought to steer the battle away from the particulars of how a pact may be structured.
"For the millions of families in America and the billions more around the world who are facing the devastating effects of the climate crisis today, the precise legal form of a global climate deal is not the key issue," said Sierra Club President Michael Brune.
The Obama administration, for its part, said it's too early to say whether the new United Nations climate pact that international negotiators hope to finalize in Paris late next year will require Senate sign-off.