British Prime Minister Theresa May has told lawmakers she may not seek passage of her troubled Brexit withdrawal plan in Parliament next week.

The embattled leader, who faces a major protest march in central London on Saturday, wrote to lawmakers Friday night saying she would bring the European Union withdrawal back to Parliament if there seems to be enough backing for it to pass.

“If it appears that there is not sufficient support to bring the deal back next week, or the House rejects it again, we can ask for another extension before 12 April, but that will involve holding European Parliament elections,” she said.

May’s changing stance reflects the plan’s dismal chances in the House of Commons after two prior defeats.

She also says she would need the approval of House Speaker John Bercow to bring the plan back for a third time despite his objections. Bercow has said a third vote would violate parliamentary rules unless the plan is altered.

May said in her letter to lawmakers that if the deal is approved, Britain will leave the EU on May 22, a date agreed with EU officials.

Lawmakers have twice rejected the deal and haven’t shown any clear swing toward endorsing it in recent days. Britain is scheduled to leave the European Union on April 12 if no deal is approved.

Pro-Brexit forces are also girding for the possible political impact of a planned march in central London in support of holding a second referendum that would give British voters the option of remaining in the EU despite the 2016 vote in favor of leaving.

The organisers of the “People’s Vote March” predict that one of Britain’s largest-ever protest marches will grip central London.  More than 4 million people endorsed an electronic petition this week in favor of revoking Article 50, the act that formally triggered the Brexit process.