Hii!
No, you will not face any problem in government jobs after completing two courses simultaneously. There is no issue in that.
Although you haven't mentioned or tagged specifically about the type or sector of  jobs you want to join in, but let me tell you that most of the government jobs require graduation degree by the candidates and also some of them require skills.
So, you can apply into jobs as per the eligibility criteria and you will nit face any problem.
Hope this helps.
Good luck!