What problems did the National Convention face? How did this problem impact how revolutionary leaders began to treat suspected traitors within France?

The first problem was the extremely hostile reaction of European monarchies towards the new republic. Indeed, France had wavered between the adoption of a Constitutional Monarchy like the one in Great Britain and a republic more or less styled after the American Republic. These monarchic European armies had invaded part of the French territory and were making preparations to invade others. Great Britain was especially hostile and it certainly took advantage of the fledging French democracy to lead all external belligerence against it and organize internal royalist insurrections.

The second problem was internal divisions in both the country and the government. In the government, the more business-oriented and provincial bourgeois elements were the Girondins and the more fiercely republican, Parisian, and populist ones were the Montagnards. There was also the radical extreme faction of the Jacobins. Concerning the country, the large and strategic region of Brittany was largely royalist and Catholic and they were funded and supported by Great Britain and were engaged in a guerrilla war against the National Convention.

Because of so many threats and divisions, an atmosphere of fear and mistrust was prevalent and such emotions encourage the extremism of both parties. In a context of internal insurgency and external military threat, fear of royalist agents and foreign spies was at an all-time high and this resulted in the Terror period, when the Jacobins seized power and started arresting and executing every man or woman suspected of counter-revolutionary activities.