If you listened to President Barack Obama and incoming Senate Majority Leader Mitch McConnell Wednesday, you may feel hopeful at the prospect of a functioning Congress. “[McConnell] has always been very straightforward with me,” the president said. “To his credit, he has never made a promise that he couldn’t deliver.” McConnell was similarly optimistic about the 114th Congress. “There’s only one Democrat who counts—the president,” he said. “He’s a player. That’s the way our system works.”

Don’t believe them. Obama and McConnell may be talking nice but their statements are incompatible with their political and policy agendas. They are on a major collision course—and the inevitable fallout is very unclear.

The clearest divide between the White House and GOP senate is over immigration. At his press conference Wednesday, Obama reiterated his commitment to taking executive action on immigration before New Year’s. “What I’m not going to do is just wait,” he said. “I think it’s fair to say I’ve shown a lot of patience and tried to work on a bipartisan basis as much as possible, and I’m going to continue to do so. But in the meantime, let’s see what we can do lawfully through executive actions to improve the functioning of the system.” We still don’t know what that executive action will entail, or whether Obama will scale it back after Tuesday’s election results. But it seems clear that the president intends to do something on immigration.

For Republicans, any unilateral action on immigration is a grotesque offense. As McConnell said Wednesday, “It’s like waving a red flag in front of a bull. … I hope he won't do that because I do think it poisons the well for the opportunity to address a very important domestic issue." In other words, immigration reform may be dead before the 114th Congress even starts. So much for bipartisanship.

McConnell may plan to do more than just denounce Obama’s executive action. In a letter to Majority Leader Harry Reid, five GOP senators said they would “use all procedural means necessary” to stop Obama’s executive action on immigration. It’s not immediately clear what that means, but Republicans could try to attach a policy rider to key spending bills to block the move. Senate Democrats could filibuster those appropriations bills or, alternatively, Obama could veto them. Either way, that would set up a major confrontation.

An even larger fight lurks in the future, if McConnell so chooses. The soon-to-be majority leader could use the budget process to force a filibuster-proof vote on major provisions of Obamacare. Senator Ted Cruz is the leading advocate of this strategy. Will McConnell follow it? Maybe. Last week, his spokesperson said, “[McConnell] believes that if Republicans are fortunate enough to take back the majority we’ll owe it to the American people to try through votes on full repeal, the bill’s most onerous provisions, and reconciliation.” In a joint op-ed in the Wall Street Journal Wednesday, McConnell and House Speaker John Boehner reiterated their commitment to repealing the law.

If Republicans use the reconciliation process to undermine Obamacare, the president would surely veto the bills, setting up a potential government shutdown. But McConnell also said at his press conference that “there will be no government shutdown and no default on the national debt.” If McConnell isn’t willing to shut down the government, then he has lost his only leverage to demand policy concessions—like repealing major provisions of the Affordable Care Act—from the president.

Something has to give. If Republicans intend to govern, they will have to work with the president, even if he takes executive action on immigration. And if they want to undermine Obamacare, then they have to be willing to shut down the government. McConnell or Obama could relent and avoid this fight. But based on their words this week, that seems unlikely. In that case, no amount of niceties changes the basic math that a collision is coming.