Britain was supposed to have left the European Union on Friday but Brussels let London delay its departure while May battles to try to secure a consensus on how and when to leave the bloc.
The rising uncertainty has battered sentiment towards the pound after some optimism that the United Kingdom would successfully avoid crashing out of the EU without a deal bolstered the British currency in recent weeks.
"Even if she manages to win the vote today, which looks like a very long shot, the uncertainty over the pound will remain," said a trader at a European Bank in London.
Parliament will vote on a stripped-down version of May's twice-defeated divorce deal agreed with Brussels on Friday. Even if she wins, another vote will be required for Britain to legally exit the EU and the uncertainty is dismaying investors.
Britain's attorney general said the vote was the last opportunity for Britain to take advantage of its legal right of delaying Brexit until May 22. Should the deal not be approved the Brexit delay will expire on April 11, Geoffrey Cox said.
The stance of Northern Ireland's Democratic Unionist Party, which props up May's minority government, has been that it cannot back a Brexit divorce deal that does not protect the whole of the United Kingdom, and the DUP said on Friday that "still stands and is our position".
Traders are sticking to the sidelines, creating a shortage in liquidity in the market that has exacerbated swings in the pound.
Volatility gauges for the pound in the short term relative to the medium term are at their highest levels since the Brexit referendum vote in 2016, indicating traders remain nervous.
Prominent critics, including Northern Ireland's DUP and Conservative eurosceptic hardliners who seek a complete break from the EU, have refused to back the transition deal, meaning May had little chance of winning a parliamentary majority.
However, a Sun Newspaper report that former Brexit secretary Dominic Raab and other hardliners previously opposed to the deal may now be willing to support it, briefly lifted the pound to the day's high of $1.3135.
"On the one hand, it's another prolonged period of economic uncertainty, but one after which we could end up with a softer Brexit than that on offer, or none at all," said Craig Erlam, an analyst at OANDA.
The currency rallied as much as 0.7 percent before trimming some gains to stand 0.4 percent up on the day at $1.3095. It was up 0.4 percent against the euro at 85.75 pence.