With three closely watched regional elections looming in March, Merkel is facing the toughest spell of her 10-year chancellorship over her handling of the refugee crisis.
Conservative allies in Bavaria, the entry point for most migrants, are regularly breaking ranks and criticism is also mounting from her Social Democrat (SPD) coalition partners.
Some media have even started to speculate about Merkel's future.
An INSA poll in Tuesday's top-selling Bild newspaper showed support for Merkel's conservative bloc down 2.5 percentage points at 32.5 percent, its lowest since the 2013 election.
It also put the right-wing Alternative for Germany (AfD), which campaigns against refugees, up 1 point at 12.5 percent.
The AfD has gained from worries about migrants, exacerbated by sexual attacks on women in Cologne and other cities at New Year, blamed largely on asylum seekers and is likely to make big gains in elections in three states in March.
"There's a clear trend against conservatives in Germany. Time is short to turn this sentiment round before the regional votes in March," INSA chief Hermann Binkert told Bild.
Merkel's insistence that Germany will cope with the influx of 1.1 million migrants last year and more this year, has angered local authorities struggling to house people, many fleeing war zones in Syria and other Middle East countries.
Pressure is mounting on her to shut the borders five months after Germany opened its doors to asylum seekers from Syria, effectively suspending EU rules.
In a letter to Merkel, 44 conservatives - many from her own Christian Democrats (CDU) as well as Bavaria's Christian Social Union (CSU) - urged Merkel to change course.
"We are facing excessive demands on our country. We believe a change is urgently needed in current migration practice ... by a return to the strict use of existing law," states the letter.
One of the initiators of the letter told Reuters a total of about 100 conservative lawmakers backed it.
It comes after Germany's transport minister urged Merkel on Monday to prepare to close Germany's borders to stem the influx, a highly unusual move for a cabinet member.
The letter is just the latest headache for Merkel. The CSU wants a cap on migrants and some members are talking about taking the government to the Constitutional Court.
The Social Democrats (SPD), at odds with conservatives on planned new rules on migrants, are also stepping up criticism.
"It is not on if Mrs Merkel lets herself be cheered for inviting over one million refugees ... while her CDU bows out of responsibility for long-term integration," SPD Chairman Sigmar Gabriel said this week in an unusual dig at his boss.
Conservatives fear Merkel's attempts to persuade other EU countries to take in quotas of refugees, push for reception centres to be built on Europe's external borders and pay Turkey to keep refugees from entering the bloc are not working.
There are signs that Merkel, traditionally known for her pragmatic approach, is hearing at least some of the criticism but she has remained firm in resisting a cap.