The Government also tried to pressure resistant MPs by saying their refusal to fall in line could result in Britain remaining a member of the EU.
Brexit Secretary Steve Barclay warned that Parliament could block Brexit altogether.
May's office also said it was "extremely concerned" about reports that some MPs would try to seize control of Brexit negotiations if the agreement May's Government reached with the EU is defeated.
The Sunday Times reported that senior MPs intend to try to change the rules of the House of Commons so they can wrest control of the legislative agenda from the Government.
The Prime Minister faces widespread opposition to the existing agreement, primarily because of language designed to prevent the reintroduction of physical border controls between Northern Ireland and Ireland.
MPs on all sides of the Brexit debate fear the so-called Northern Ireland backstop could leave Britain tied to the EU indefinitely.
May postponed a vote on the deal in mid-December when a resounding defeat was clear. She now is urging Parliament to support it so Britain doesn't leave the EU on March 29 without a deal, which would threaten trade, jobs and economic growth.
While a majority of the 650-seat House of Commons appears to oppose leaving the EU with no deal, there is no agreement on what alternative to pursue.
Straw polls show more than 200 MPs back May's deal, while about 100 support a no-deal Brexit and other factions advocate a "soft Brexit" that keeps Britain close to the EU or a second referendum.
The BBC estimates that May's deal is likely to be supported by about 240 MPs, far short of the number needed for passage.
As evidence for the claim that MPs might block Brexit, Barclay cited a parliamentary vote last week that will push the Government to come up with a Plan B within three working days if May's deal fails. That's much sooner than would have otherwise been the case.
"Uncertainty in terms of what will happen in the House has increased," Barclay told the BBC. "So those on the Brexiteer side seeking ideological purity with a deal are risking Brexit, because there is a growing risk that events could unfold in ways that (mean) they are leaving the door ajar to ways that increase the risk to Brexit."
At the very least, there is a growing chance Parliament may seek to postpone Britain's departure date while politicians work on a new plan. The Guardian reported that the EU is preparing to delay Brexit until at least July.
Michael Roth, a German deputy foreign minister, was quoted as telling the Frankfurter Allgemeine Sonntagszeitung that if the British Government asked for an extension to Britain's withdrawal date, "we will treat it very responsibly."
But he added that it would pose "quite complicated questions, such as Britain's participation in the European election".
The Guardian reported that the deadline "is now regarded by Brussels as highly unlikely to be met" and the EU is "expecting a request from London to extend article 50 in the coming weeks".
It says that a leaders' summit to push back Brexit is expected to be convened once a British request is received.
British Opposition Leader Jeremy Corbyn said the Labour Party will seek to force a general election if Parliament rejects May's deal.
He suggested that he might force a vote of no-confidence "soon." If that effort were successful, Labour would likely also request a delay in the Brexit process.
"Clearly, if a general election takes place and a Labour Party government comes in...there would have to be time for those negotiations,' Corbyn said.
- AP
