Solna municipal commissioner Pehr Granfalk expressed his desire for her to walk on Tuesday, telling public broadcaster Sveriges radio:
"I don't think she has become any clearer. She has failed to convey the party's policies in a better way, and that's also reflected in the opinion polls, so for me confidence is broken".
Kävlinge municipal council chairperson Pia Almström joined him in that sentiment meanwhile.
"There have been attempts to rethink, but it hasn't produced results and it's not working. I'm deeply worried," she told newspaper Dagens Industri (DI).
According to DI there is an internal dissatisfaction with the leader in the party, and more calls for her to go are expected on Wednesday. One source of those could come from the Moderate youth wing (Moderaternas ungdomsförbud, MUF), which after a conference call on Tuesday was given the go-ahead to come out demanding Kinberg Batra's departure.
"It will happen tomorrow," a source told Expressen on Tuesday.
Sweden's four centre-right Alliance parties are polling at 37 percent these days, a decrease of 1.4 percentage points from June, while the coalition government combined with traditional allies the Left Party are polling at 42 percent, an increase of 0.9 percentage points according to an Ipsos poll in Dagens Nyheter.
In particular the centre-right parties appear to have failed to take advantage of the governent's handling of the recent IT scandal at Sweden’s Tranport Agency.
This is the second time in a short period that voices within the Moderates have called for their leader to go. The same happened in May, leading Kinberg Batra to admit that she was "in the midst of a crisis of confidence, as are we as a party".
Her response was to replace one of the party’s most prominent figures, former spokesperson on legal affairs Beatrice Ask, who was previously Sweden’s justice minister.
When news agency TT sought out Kinberg Batra for comment this week, they were instead referred to party secretary Anders Edholm, who insisted she will be the one leading them into the 2018 election:
"We are a big party with different opinions and it’s a shame that some municipal politicians are focusing on resignation demands when we should be focusing on winning confidence. Of course there’s a concern when it’s not going well in opinion polls, but it is obvious that Anna Kinberg Batra has grown and we as a party are working fully to win her the confidence of more voters".