– A small but influential party aligned with Prime Minister Theresa May's government suggested Friday it still cannot support her plan for Britain's departure from the European Union, a development that could doom her hopes of persuading Parliament to pass the deal next week on the third try.

The Democratic Unionist Party of Northern Ireland holds just 10 seats in the 650-seat House of Commons. But the central sticking point in the talks on a British withdrawal has been how to handle the border between Northern Ireland and Ireland, and the party's position carries disproportionate weight with others in Parliament.

Parliament has twice rejected the agreement that May negotiated with the European Union for Britain's departure, and both times the DUP has voted against it, largely because of concerns about the border issue.

If Parliament rejects the deal again, there is still the possibility of a cliff-edge Brexit in the short term or a much longer delay to renegotiate the agreement to leave.

May's position appears to grow more precarious by the day — not only her chances of winning approval of the Brexit deal, but her hold on power. Long-standing talk that she could be ousted by her own party, or by Parliament as a whole, has intensified, becoming a constant rumble in the background to everything she says or does.

On Tuesday, House of Commons Speaker John Bercow ruled she could not have a third vote without a substantive change to her plan. On Wednesday, she delivered a speech blaming the paralysis on Parliament, angering lawmakers on all sides.

On Thursday, E.U. leaders agreed to postpone the March 29 departure date but refused the prime minister's request for a three-month delay, only giving her until next week to win parliamentary approval for her deal or come up with some alternative by April 12. If her deal is agreed to by Parliament, Britain's exit will be pushed back to May 22. On Friday came the blow from the DUP.