Several Tory MPs have expressed disquiet over the bill but are expected to back it at second reading, the first stage of its progress through the Commons.
The government has rejected suggestions of a "power grab".
Tom Brake, Lib Dem Brexit spokesman, said MPs who backed the Bill should feel "ashamed".
Labour leader Jeremy Corbyn suffers substantial rebellion among MPs in Leave-voting areas.
The bill, which transposes European Union law into British law, now moves onto its next Parliamentary stage.
Guy Verhofstadt told reporters in Strasbourg that Ms May and MEPs should have an "open dialogue" with MEPs to discuss the issues because the European Parliament would ultimately have a vote on whether to agreed the final deal.
I believe Flint spoke for many when she questioned Labour's outright opposition to the Bill whilst pointing out the need to modify the checks and balances contained within it.
At least one Labour MP joined Conservative and DUP MPs who pushed the bill through, after warnings that rejecting the bill would be unpopular in Leave-voting communities who would see it as frustrating their choice.
The Liberal Democrats and Scottish National Party also said they'd seek changes.
"This is likely to cause delays and division in Parliament, and the Prime Minister has nobody to blame but herself", SIr Keir said.
"Providing certainty and stability in the lead up to our withdrawal is a key priority", he said.More news: President Trump on Hurricane Irma: 'We've never seen anything like this'
"They will go some way to improve what is a deeply flawed Bill".
However, the gun is still loaded and if serious changes are not made as MPs in committees dissect the bill line by line, it may yet be used. Although a number of Conservative lawmakers had threatened to rebel, no members of the governing party voted against the measure.
Neil Carberry, managing director for people and infrastructure at the Confederation of British Industry (CBI), said he hopes there will be changes to the government's approach when it publishes its official position in the next couple of months.
The bill, which will end the supremacy of European Union law in the United Kingdom, now moves onto its next parliamentary stage.
They feel the lesson of the protracted Maastricht process is that you should vote for the principle of the Bill so it is harder to accuse you of sabotage...and only then should you tie the government up in knots on amendments (there were some 600 or so over Maastricht).
Remain campaigner Stephen Kinnock warned that "power corrupts and absolute power corrupts absolutely", adding that May was attempting to grab a unsafe level of power to rewrite or scrap long-standing laws and rights.
The government has defended the bill by saying it will allow Britain to become "masters of our own laws", but it also gives ministers wide-ranging powers to amend laws to make them work domestically, often by interchanging the word "EU" for Britain.
However, others were more positive about the bill.
Corbyn, who for most of his political career has opposed British membership of the European Union, was persuaded by his party to campaign against Brexit in 2016.
"Brexit, through this bill, is a chance to reignite the ability to enthrall through politics, law and justice", she told MPs.