She'd be ripping up her guarantee to support the PM in the commons.
If the DUP votes against the budget, which will be presented on October 29, this could trigger a confidence motion and a general election if the government loses. Despite their abstention, it was still defeated by 59 votes.
In addition, Northern Ireland would remain under large parts of single market regulations, requiring enhanced checks on products arriving from Britain, particularly agricultural goods.
DUP leader Arlene Foster insisted on Tuesday that her party would not accept customs or regulatory checks on goods travelling in either direction between Northern Ireland and Great Britain after meeting EU chief negotiator Michel Barnier in Brussels, and again following talks on Wednesday with European Parliament Brexit co-ordinator Guy Verhofstadt.
The nature of those criteria, and additional language to be used about the future deal, required by the United Kingdom to assuage concerns about the ultimate need for such a backstop solution to avoid a hard border on the island of Ireland, are still open to debate. It would have implications not just for Brexit legislation - 50% of which would not have passed without DUP support - but also for the Budget, welfare reform and other domestic legislation.
Despite his calls for major shift in the UK's negotiating position, Barnier claimed a Brexit deal could be agreed by next Wednesday's European Council summit.
The DUP has 10 MPs, although Ian Paisley can not vote in the Commons until November 20 after being suspended for failing to declare two family holidays paid for by the Sri Lankan government. Downing Street earlier warned there were "big issues still to resolve".
May gathered selected members of her cabinet late Thursday to update them on the Brexit talks, and the Financial Times reported that she told them that a deal was drawing closer.
But Cabinet sources said senior ministers were expected to consider the backstop plan when they met this afternoon with a view to getting the backing of the full Cabinet next Tuesday.
Speaking to Sky News in his constituency of Larne on Northern Ireland's east coast, Mr Wilson said that the DUP were not going to be "bullied" or "bribed" into supporting a deal that could see Northern Ireland effectively kept in the single market or customs union.
Theresa May has been put on notice by her allies in the Democratic Unionist Party to change course on Brexit or risk the collapse of her government.