A group in the DA tried to convince the party to pull out of coalition governments with the EFF in Tshwane and Johannesburg.
The plan was abandoned after it failed to secure enough support to carry it through to the DA's urgent federal executive meeting held on Wednesday.
DA insiders who spoke to the Sunday Times on condition of anonymity said there was growing unhappiness with the role that the EFF was playing in these coalitions, especially its threat to remove the DA from power when the parties disagreed.
Concerns were also raised about the manner in which Johannesburg mayor Herman Mashaba was said to readily give in to EFF demands.
The plan came after the EFF teamed up with the ANC in an attempt to remove Tshwane mayor Solly Msimanga through a motion of no confidence just a few days after it helped vote out Athol Trollip as mayor in Nelson Mandela Bay.
"They were angry after the removal of Trollip and wanted to argue that we can't continue being in coalition with the racist EFF.
"But most of them did not go to [the federal executive committee] because they knew they were going to be defeated there," said a party insider who knew of the plans.
Another DA leader who attended the federal executive meeting said only Gauteng MPL Kate Lorimer raised the matter at the meeting.
The leader said Lorimer did not get support because her usual backers were not at the meeting.
"There was one individual, Kate Lorimer, who hinted when she gave her input that 'maybe we should think about' pulling out of the municipalities. She didn't have her normal supporters at the [federal executive]."
The insider said Lorimer has long-standing problems with how the DA was doing in the City of Johannesburg, where Mashaba is seen as overly close to the EFF.
"[She said] the tail is wagging the dog, maybe we should put our foot down and say that we will not allow the tail to wag the dog.
"She has a problem with Mashaba because Herman consults. They have a problem with him because they want to control him, the 'laptop boys'. But nobody controls Herman," said the DA leader in reference to Lorimer and the party's liberal faction.
Lorimer declined to comment, saying federal executive discussions were confidential.
Party leader Mmusi Maimane, after hearing of plans to call for a withdrawal from the coalition governments, is said to have quashed such talk with his opening speech at the meeting. 
Another insider said: "He pre-empted [that the call to pull out of coalitions] was going to be raised and told the meeting that the DA was not going to pull out. If the EFF was going to vote the party [out of power in Tshwane], then let it be."
Msimanga survived a dual motion of no confidence brought by the EFF and the ANC on Thursday.
DA spokesperson Solly Malatsi said the federal executive was unanimous in its resolution to continue to lead the coalition governments, no matter how difficult the current circumstances.
"The DA remains committed to working with parties which are prepared to root out corruption in our metros.
"The DA-led coalition governments inherited a mess from years of ANC looting of public money. Now it is our mission to ensure that we continue with the work of government that the voters entrusted us with in 2016," he said.
"Our broad framework with any party is that we root out corruption.
"If the EFF is committed to eradicating corruption, delivering services and ensuring South Africans have fair access to work, we will work with them," he said.
He said Maimane had met coalition partners this week to firm up the DA's position on the matter and had written to the EFF leadership to meet and discuss the future of metros.
Meanwhile, an EFF leader, speaking on condition of anonymity, said Msimanga was going nowhere. He said the EFF had tabled the motion to remind the DA which party ultimately held power, but would never return Tshwane to the ANC.
"The EFF is not in the business of removing that guy [Msimanga]. If we wanted, we would have removed him."
The leader said the EFF was even being lobbied by some ANC members as late as Wednesday not to support ANC regional chairperson Kgoshi Maepa for mayor should Msimanga be removed.
"How do you vote for a party which can't get its own house in order?"..