The YouGov survey published Wednesday found that 47 percent of those polled wanted to see Merkel step down ahead of her term end as opposed to only 36 percent who wanted her to complete her term.
Support for Merkel was stronger shortly after the parliamentary elections in October. A YouGov survey at the time found only 36 percent of voters in favor of an early departure for Merkel compared to 44 who wanted her to stay in office.
Coalition talks between Merkel's conservative bloc and the center-left Social Democrats are to start on Jan. 7, which could result in either a repeat of the last so-called grand coalition or a minority government led by Merkel.
A complete failure in the talks, however, could see early elections in 2018.