On Tuesday, the U.K. House of Commons soundly rejected Prime Minister Theresa May’s carefully negotiated Brexit deal. On Wednesday, they also rejected a vote of no confidence, instead choosing to keep May and her government in power.

That's one win and one loss for May and a whole lot of confusion in Westminster.

That political whiplash also means that 2.5 years after the Brits narrowly voted to leave the European Union, lawmakers still have no consensus on what Brexit means or what they would want from a potential deal. Some think the U.K. should try to get itself out of the Brexit stalemate the same way it entered it: with a new referendum.

But the truism of Brexit is that everything is not as simple as it seems, and that applies to a second referendum as well.

First, a new vote would have to be approved by Parliament.

That’s likely to be met with significant opposition. For pro-Brexit members, even putting the proposal before voters again is a no-go. In their view, the people already made their voice heard, and the government must act. Theresa May, who has called the possibility of a second Brexit referendum a "gross betrayal" of democracy, also opposes the vote.

Even if the government could reach an agreement to put Brexit before voters again, the exact wording of the question would also have to be approved by Parliament, setting the stage for more political wrangling and finger-pointing. Then, the question would go to the Electoral Commission, which decides if such questions are intelligible and free from bias. The commission would likely propose revisions which would then also have to be approved by Parliament.

Moreover, the whole process of getting a second referendum in place would likely take at least 21 weeks. That would run well past the March 29 deadline when the U.K., now by default, leaves the EU. That timeline means that Parliament would have to extend Article 50 (the provision of the Treaty on European Union that allows countries to exit the EU).

That, too, is not as easy as it sounds. First, Parliament would need to vote to instruct the government to request an extension. Then, the government would have to signal to the EU that the extension would pave the way for a different, better approach than the current failed negotiations and thus be worth accepting. Finally, the 27 other EU member countries would have to accept the request.

If Parliament cleared all those hurdles, even a new vote might not yield a clear path forward.

Although unlikely based on recent polling, the “leave” camp could also win again, prompting another round of the same parliamentary brawling. On the other hand, a successful but not overwhelmingly victory for remaining in the EU would still likely yield more political wrangling and potentially legal challenges to the ability of the U.K. to go back on the already-invoked Article 50 — although the current consensus seems to be that it could.

The bottom line is that the U.K. is on no less a solid path for Brexit than it was before. The "simple" approach of asking the people again would still lead to more parliamentary chaos.