Of course they had difficulties converting the population, otherwise the Germans would not have been the first people to rise up against the Sovjets and their local puppets. With the Uprising of June, 17th started by the workers, the population essentially took control of the GDR, the communist government fled into the soviet barracks, etc. and they demanded reunification. As an example the demands the people of the county of Bitterfeld sent to the government:...So after the war did the newly installed communists under Stalin have difficulty converting the population to a system of government they viewed as anathema to them?..
1. Resignation of the so-called German Democratic Government, which made itself come into power by election maneuvers
2. Formation of a provisional government by progressive working people
3. Permission of all big parties of West Germany
4. Free, secret and direct elections in 4 month time
5. Release of all political prisoners (straightforward political, so-called economic criminals and denominational prisoners)
6. Immediate abolition of the Zone Frontier and the withdrawal of the police
7. Immediate normalization of the standard of living
8. Immediate abolishment of the so-called Peoples Army
9. No reprisals against someone on strike
If the Soviets had not sent in tanks and crushed the uprising, that would have been the end of the german divison. After this event the east german government never trusted its population again. As Bertolt Brecht put it:
"The Secretary of the Writers Union
Had flyers distributed in Stalin Way that said
That the People had frivolously
Thrown away the Government's Confidence
And that they could only regain it
Through Redoubled Work. But wouldn't it be
Simpler if the Government
Simply dissolved the People
And elected another?"
and the population rose up again in the moment it became clear that it wasn't a 100% chance any more that soviet tanks would come and ended the existence of the GDR.
Here is a video where you can see how the strikers pull down and maul the soviet flag from the Brandenburg Gate: