"We will become a Trojan Horse within the EU and utterly derail all their attempts to pursue a more federalist project," said Conservative MP Mark Francois at a Brexiteer conference in the heart of London ahead of Wednesday's critical EU summit.
"If we were to be held in the EU against our democratically expressed will because some in the EU hope against hope that we will change our mind, then they will live to regret it," he said.
May wants to push back Brexit from 12 April to 30 June to arrange Britain's orderly departure but Brussels fears that will not be long enough.
European Council president Donald Tusk's office has floated the idea of a "flexible" extension of up to one year, with an option for London to leave earlier if it finds a way through, but there is no agreement on this as yet.
EU negotiator Michel Barnier said on Tuesday that May must explain what another postponement would achieve.
"The length of the extension must be linked to the purpose, what it's for, and that depends on what May will say to European leaders on Wednesday."
May had requested only a short delay to avoid having to take part in European Parliament elections, which begin on 23 May, but a long postponement would entail Britain's participation in the polls.
This is the point that riles Brexiteers like Francois and Jacob Rees-Mogg who voted against the Brexit deal that May struck with the EU all three times it came up for a vote, viewing it as too EU-friendly.
"If a long extension leaves us stuck in the EU we should be as difficult as possible," he said.
Rees-Mogg said Britain should make best use of its predicament by vetoing "any increase in the (EU) budget, obstruct the putative EU army and block (French President Emmanuel) Macron's integrationist schemes".
Veteran EU foes such as Nigel Farage, a key face of the pro-Brexit campaign who once headed the nationalist UKIP group, hope the growing discontent will carry his new Brexit Party to big gains in Europe.
"If we have to fight those European election on 23 May, we'll fight them because it's time we taught them a lesson," Farage said in a video campaign message.