"If the government gets crushed, then you have a big risk off move," said Michael Schumacher, director of rate strategy at Wells Fargo. "If it's a close defeat, you might see equities do okay." He said there could be a big move in short-end Treasury yields if the vote and headlines around it trigger a big flight to quality.

U.S. strategists are watching the vote closely, and the outcome could be announced sometime in the afternoon east coast time. If the vote fails, May then has three days to come up with an alternative way to move forward to separate the U.K. from the European Union. She would also be at risk of a no-confidence vote, and parliament could seize the process of forming a Brexit plan.

"We could see knee-jerk volatility. She could lose by a historic margin. This could be a historic loss by the government," said Marc Chandler, Bannockburn Global Forex chief market strategist. Chandler said the U.K. government has only ever had three votes go down in parliament by more than 100 votes, and this could be a fourth.

Prime Minister Theresa May's Brexit plan is widely expected to fail in parliament Tuesday, but the defeat could still trigger a violent market reaction.

Schumacher said handicapping the aftermath of the vote is difficult, but a closer vote could signal that the government is more likely to work out a compromise exit plan. On the other hand, the public could also be given another referendum to remain in the European Union.

"It's Pandora's box. We talk to clients in the U.K. They don't know what to expect," said Schumacher.

Either way, the already volatile markets could be on edge going into the vote.

"I think it's a tough headline, but it's another step along the road of them having to come to the best agreement they can before March 29," said David Bianco, chief investment officer Americas, DWS. "Maybe when it fails it causes them to amend it a little bit, which is what we expect. We don't think they put a referendum to the public."

Sterling has been rising ahead of the vote and reached 1.293 against the dollar Monday in U.S. trading, its highest since Nov. 15.

"I think the market's a little ahead of the news media. The market has already adjusted," Chandler said. He said the wild card will be how long it will take to come up with a plan B, adding the market has probably already priced in the failed vote. The European Union is also unlikely to demand Brexit stick to its schedule, and it could be delayed while a new plan is worked out.

"Sterling got up to almost 1.30 today. A Brexit with a no-deal divorce is not the most likely scenario even if the government loses the vote, and perhaps ultimately May is right that if a withdrawal vote is rejected, it's more likely you don't get a Brexit than if you get a Brexit with no agreement," Chandler said.

Chandler said the odds have shifted away from a "no deal" Brexit in which Britain exits the E.U. with no rules or plan, hurting the economy and leaving all sorts of things, like trade with Europe, in chaos.

"In order for sterling to continue to outperform, the risk of a 'no deal' has to be minimized. Last week, an amendment passed that said they can't spend any money on preparation for a no-deal exit," Chandler said.