More than 22,900 people have signed a petition to deselect Normanton, Pontefract and Castleford MP Yvette Cooper.
The petition accuses Ms Cooper of failing to represent her constituents, and calls for her to step down as MP.
Many of those who have signed the petition left messages of dissatisfaction with the politician.
It is not clear how many of the signees live in Ms Cooper's constituency.
Richard Hampshire, who launched the petition three months ago, said: "The referendum in our constituency was a staggering 70 to 30 in leave's favour and all Yvette Cooper has done is try to block and frustrate at every opportunity.
"Now she is trying to force no deal off the table - this is totally unacceptable.
"We had a democratic vote and we wish it be respected."
Voters in the Normanton, Pontefract and Castleford constituency voted 69.29 per cent to leave in the 2016 referendum.
Yvette Cooper hit the headlines last week when she led a cross-party group of MPs in a successful attempt to force Prime Minister Theresa May to extend Article 50, and prevent a No Deal Brexit.
David Jones, constituency Labour Party Chair, said: “This petition has been spread all over the country by far right groups on social media and the vast majority of people who have signed are not from our area at all.
"Some comments on the petition have also had to be reported to the police as they have even included death threats against Yvette and other MPs.
"Most people think the Brexit process is a mess, but they want a sensible debate on sorting it out, not abuse or threats.
"The petition also doesn’t make any sense - there isn’t a national selection or deselection process.
"Theresa May’s Brexit process is a mess so thank goodness Yvette is trying to find a sensible way forward that stops local jobs or families being hit.
"Our constituency party members recognise the need to protect jobs in our constituency and support Yvette in what she is doing to avoid the chaos of a No Deal.”
The petition alone does not have the power to force Ms Cooper to step down.
Labour MPs only face deselection if 33 per cent of their constituency's local branches and affiliated unions vote for a reselection contest in a "trigger ballot".