A new website and social-media campaign have been created with a goal to "Tell Andrew that you have his back".
StandwithScheer.ca makes the case that Conservatives can only form government when their party is united.
It also accuses the media of whipping up trouble and features quotes from his supporters inside and outside of caucus.
The Conservatives won the popular vote in the last election but fell far short of winning enough seats to form government.
That's because Scheer's campaign style and socially conservative history turned off many voters in seat-rich Ontario and Quebec.
Meanwhile, another website, Conservativevictory.ca, was launched by veteran right wingers who want Scheer replaced. They include Stephen Harper's former communications director, Kory Teneycke, and former B.C. MP John Reynolds.
"We believe that Canada needs a strong Conservative Party to win the next election, and that the continued leadership of Andrew Scheer will only lead to another Liberal victory," it states.
One of Conservative Victory's spokespeople is Sara MacIntyre, a former Stephen Harper press secretary and a former B.C. director of the Canadian Taxpayers Federation.
A tweet that she put out after the election energized LGBT-friendly conservatives to call for Scheer's ouster.
Former interim leader Rona Ambrose has also tweeted her support for LGBT rights.
Both websites are collecting names and email addresses in advance of the Conservative party convention in April.