Former Brexit minister Steve Baker said up to 40 MPs were ready to vote against "a backstop that leaves us in the internal market and customs union come what may".
Asked whether she could rely on DUP votes to pass her Chequers plan, a spokesman for the Prime Minister said: "The confidence and supply arrangement that we have with the DUP is a matter of record".
Kevan Jones, MP for North Durham, told the Financial Times he would wait to see what type of deal the Prime Minister returned with, but added: "I would not support no-deal because that would be disastrous both for my constituents and the country".
The Budget takes place on 29 October.
But he also set out key objections to her proposed new trading relationship which involves a UK-EU customs partnership and a "common rulebook" for goods travelling across the border.
"The whole point about checks is that there is a difference" she said.
Rejection of any kind of special status for Northern Ireland inside the EU customs union by the DUP, which props up Mrs May's government, makes getting a deal through parliament much more challenging.
In a statement to the Commons updating MPs following a summit of EU leaders in Salzburg last month, Brexit Secretary Dominic Raab denied the United Kingdom would stay in the customs union indefinitely, and said the government would "press our case" for an outcome that will "preserve the integrity of the UK".
The DUP has constantly stated there can be no border in the Irish Sea and Northern Ireland must leave the European Union on the same terms as the UK.
EU Migration Commissioner Dimitris Avramopoulos told a press conference: 'Michel Barnier and his team are working day and night to reach a deal, but we are not there yet'.
"If we followed Mr Barnier's advice, my information is that those checks would become 100%, although with a veterinary agreement in a future trade deal, that might be reduced somewhat", she said.
But Foster refused to consider such a compromise on Tuesday, saying: "What we said to Barnier is checks of themselves are symptomatic of something different, so we only need checks if Northern Ireland is following a different regulatory regime to the rest of the UK". But he stressed: "Brexit was not our choice".
The Labour leader is expected to whip his MPs to vote against the Brexit deal when it comes to Commons, whatever the shape of the agreement as it is unlikely to meet with the party's "six tests".
The prime minister's spokesperson said government officials are in "intensive" talks with European Union negotiators in order to resolve the Irish border issue, which is the last major outstanding issue in the draft Withdrawal Agreement.