But Arlene Foster's Northern Irish block has already said it won't be supporting the deal Mrs May brought back from Brussels, so she will have to look elsewhere.
MPs will vote on Theresa May's Brexit deal on December 11 after five days of debate, the Prime Minister has confirmed.
It was a day many doubted would ever come, but May was anything but triumphant as she reported back to Parliament, which must approve the deal for it to take effect.
Britain was scheduled to leave the economic and political union on March 29, 2019.
The nearly 800-word message is an attempt to speak directly to the public to build support for her deal, which faces widespread opposition at Westminster including from both wings of her Conservative Party and the Democratic Unionist Party which props up her administration.
This leaves her about 66 votes short of getting the deal through Parliament with a majority.
"Given there are some 80 Conservative backbenchers who will vote against any deal come what may, in the national interest will the Prime Minister sit down with the leader of the Opposition and have a meaningful discussion about how we can make sure that, when it comes to workers' rights, health and safety, we don't fall behind and we secure a sustainable customs arrangement?"
Mrs May said MPs faced a choice: "We can back this deal, deliver on the vote of the referendum and move on to building a brighter future of opportunity and prosperity for all our people".
But nothing in the negotiations has gone smoothly and the summit risked being derailed by a late objection to the deal by Spain over the British territory of Gibraltar.
European Commission president Jean-Claude Juncker warned that there would be no more negotiation if MPs vote down the agreement, telling the BBC: "This is the best deal for Britain. and this is the only deal possible, so if the House says no, we would have no deal".
Liberal Democrat leader and People's Vote campaigner Sir Vince Cable said: "If anything, the bleak predictions contained in this report are an under-estimate of severe damage our economy will suffer in the future of this deal goes ahead because it takes no account of the draining away of confidence in business and the impact on investors who no longer see the United Kingdom as a gateway to Europe".
"Jeremy Corbyn has also reassured Labour MPs that his priority is to avoid a no-deal Brexit".
She said: "I'm interested she has indicated Jeremy Corbyn is clear we should leave the European Union with a deal as previously he had indicated he would vote against any deal the Government brought forward".
Dozens of Conservative legislators say they will reject the deal, either because they want a harder or a softer break with the EU. "They failed in the Withdrawal Agreement, and they failed again in the Political Declaration", May said.