I mean was there a time where the question was raised of whether Christians should break away from the Old Testament, and if so when was it decisively overruled?
The Marcionites raised the question in the 2nd century. They believed that the father of Jesus was a separate, higher deity than the creator Yahweh worshipped by the Jews, who they saw as a legalistic and unforgiving tyrant. Most of what Jesus taught was held to be incompatible with the cruel justice and jealousy they saw in the Hebrew Bible. This is set out in Marcion's Antitheses, which I would link to if I weren't on mobile. Jesus had been sent to reveal the unknown higher god and offer people an escape from the corrupt material world.
These guys made the first attested Christian canon, with a version of the gospel of Luke and most of the canonical Pauline letters, and they were the first to definitively separate Christian and Jewish scriptures. Paul was their main apostle - the ones in Jerusalem never comprehended the true meaning of Jesus. They believed the Old Testament was 'true' and that the Law was valid to the Jews, but had nothing to do with Christians.
The question was probably decisively settled as a way to deal with this "heresy" by the church fathers, although I don't know when we could say that the decision was made.
/u/RedPurpleBlack is mostly right about the issue that Marcion creates for the early church. Marcion is an influential leader whose views pit Old Testament against New Testament in a radical way, and Marcion was significant enough to have Marcionite communities form and persist for at least a little while with his non-mainstream views.
However, I'd like to suggest that the question never really got going in the way your question suggests it might have, simply because of the nature of the New Testament. Continually through the NT texts that are canonical for Christianity there are claims that the events around Jesus are 'according to the scriptures', which in context must be the OT Canon. The whole ability of early Christians to articulate the significance of this Jesus figure is predicated on the acceptance of the OT canon.
So, to jettison that canon would render much of the NT unintelligible. Despite the early church rapidly shifting away from a Jewish demography, it's virtually impossible to read the NT without the acknowledge of the OT.