In particular, she still has to work with CSU leader and German Interior Minister Seehofer, with whom she has had several showdowns on different aspects of migrant policy.
Senior CSU figures, including Mr Dobrindt, immediately tried to persuade Mr Seehofer not to quit.
Alternatively, it could break up the two parties' 70-year partnership, depriving Merkel of her majority in parliament and pitching Germany into uncharted political waters.
The deal also requires support from the Social Democrats, the third party in Merkel's government.
On Sunday evening, the CDU passed a resolution supporting Mrs Merkel's position on migration.
CDU general secretary Annegret Kramp-Karrenbauer said in Berlin party leaders were "united" behind "effective, humane solutions together with our European partners".
However, after a night of high drama, Seehofer later said he would hold last-ditch talks with Merkel's Christian Democratic Union (CDU) "in hopes of reaching an understanding".
What did Mrs Merkel negotiate with the EU?
Leaders said they would consider setting up "disembarkation platforms" outside the European Union, most likely in North Africa, in a bid to discourage migrants and refugees boarding EU-bound smuggler boats.
Seehofer, a long-time Merkel critic, had openly challenged her with a plan to order border police to unilaterally shutter German border crossings with Austria to many asylum seekers, effectively daring the chancellor to fire him. Merkel said for her part that Germany will establish transit centers from which migrants will be returned to countries they were in earlier.
Supporters of German AfD wave flags in front of the Brandenburg Gate in Berlin, Germany, Sunday, May 27, 2018.
The flashpoint issue was Seehofer's demand to order German border police to immediately turn back all asylum seekers already registered elsewhere in the European Union, and his threat to do so against Merkel's wishes.
But the CSU and CDU together form a center-right force that has dominated national politics for decades.
In the first five months of this year, roughly 4,600 "unauthorized entries" were recorded at Germany's border with Austria, according to the German police.
Before the refugee crisis of 2015, Seehofer was mainly concerned with regional pet projects tolerated by Merkel, such as rewarding mothers who raise young children at home with state benefits and charging foreign motorists for using Germany's Autobahn. Last week, an FG Wahlen survey said 91% favour European solutions on migration, an endorsement of Merkel's line and a snub to Bavaria's nationalist push for unilateral border measures.
German Chancellor Angela Markel on Monday balked on her signature immigration policies in a bid to stay in power, agreeing to create border camps for migrants and enforce tighter border control.