Under-pressure Northern Ireland Secretary Karen Bradley is to face a vote of no confidence from her local party over her Brexit voting record.
Conservatives in Mrs Bradley's Staffordshire Moorlands constituency are angry about her support for a delay to Brexit.
The embattled Cabinet minister has already faced calls to resign this month for stating in the House of Commons that killings carried out by the security forces during the Troubles were "not crimes".
She later apologised to the families of victims in a highly public and humiliating U-turn.
Mrs Bradley was also criticised in September for admitting she did not know that nationalists did not vote for unionists and vice versa when she took charge of Northern Ireland.
The Stoke Sentinel reported that Mike Howson, of the Moorlands Conservative Association, wants a vote of no confidence in her at organisation's annual general meeting this Friday, or as soon as possible.
"There are a lot of people angry at how our MP has voted, especially to extend Article 50, over the Brexit debate," he said.
Another member, Ross Ward, said any such vote would have to be taken in a separate session after the meeting.
The criticism comes as Prime Minister Theresa May, who counts Mrs Bradley among her dwindling number of supporters, confirmed she would step down if her Brexit deal was approved by Parliament.
Mrs Bradley said: "I have received many emails from constituents concerning my voting record and would like to clarify the situation.
"I recognise votes in Parliament can be complicated, and it has been extremely difficult to follow. My objective throughout the Brexit process has been to respect the result of the referendum and see the UK leave the EU."
She said she voted to leave the EU on March 29 with the Government's deal, which was rejected by the House of Commons.
"The Commons then held votes to determine whether we were prepared to leave without a deal," Mrs Bradley added.
"Some MPs want to take no-deal off the table altogether and, while I think we should leave with a deal, I recognise that keeping no-deal on the table helps our negotiating position, so I voted against taking no-deal off the table."
The Northern Ireland Secretary said she opposed a second referendum but "it has become clear" there will be no Brexit at all unless there is a delay.
"This time I voted for a motion that asks the EU for a short extension to Article 50. This is not to keep the UK in, but to make sure we can leave with a deal," she said. "If we don't get this deal through, it is not the case that we will leave without a deal - we won't leave at all.
"This vote gives time to get agreement and ensure Brexit happens."
She said all her votes were consistent with the Conservative Party's manifesto and her focus was to get a majority of MPs to back the deal to let the UK leave "as soon as possible".