The women are yet to announce their positions on the draft treaty but a source said that this month they separately told Swiss parties at closed-door talks they could not support it at the moment, given misgivings about it across the country's political spectrum.
The source said the current cabinet is itself split on the issue and lacks a majority on the pact, a situation unlikely to change if the debate stretches into next year.
The government is due to decide on Friday whether to support the draft that streamlines ties with the EU, Switzerland's top trading partner.
The anti-immigration Swiss People's Party (SVP) is pushing to cancel freedom of movement for European workers.
The stalemate over the deal has escalated as the EU says it could deny recognition of Swiss stock market rules to gain leverage, prompting the Swiss to threaten retaliatory measures that could affect trading on Europe's fourth-largest bourse.
Keller-Sutter, who replaces pro-Europe party colleague Johann Schneider-Ammann, has said any pact must have broad domestic political support, including from labour, which opposes a deal for fear it could dilute wage protections.
"I can't rule out that if there's no agreement, we may have to pay the price with certain harassment" from the EU, Keller-Sutter told the newspaper Neue Zuercher Zeitung. "We might just have to take it."
Amherd replaces Doris Leuthard, a pro-Europe CVP member who on Wednesday warned that Switzerland delays a deal at its own peril.
"The longer we don't find an agreement with the EU, the higher the price will be," Leuthard told parliament.
Amherd has said a deal with Europe should not come at the expense of wage protections but saw room for compromise.
"I don't have any wishes for what they'll do," Amherd said. "They'll make their decision based on documents that I haven't seen yet. I'll respect their decision, and I'll use that to make my own decisions when it's necessary." (Additional reporting by Michael Shields Editing by Matthew Mpoke Bigg)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)