The government should be primarily focused on making sure its country is happily and gainfully employed. A country that is working is a country that is prospering, work means money and commerce which means an active economy. It's a trickle down effect. So, yes, I believe the government should be focused on job creation.
I do not believe governments should be primarily focused on job creation for its people. Firstly, its impossible for a government to have a primary focus since all of the problems are brought together in the government. The urgency of some things certainly ousts job creation at times. Secondly, governments can't create jobs on their own, unless they're expanding their hiring practices, so governments "creating" jobs isn't actually an accurate way of saying it.
It's not the government's job to create jobs. Jobs should be created by needs within the population, and driven by that. A government exists to help create and maintain a society, so that it does not fall into anarchy. For example, the judicial system is there to create laws; the Supreme Court exists to make sure laws abide by the Constitution. The government was not created to get highly involved in the lives of the American people, and should not be focused on job creation.
It is hard to say that there is only one primary focus for the government. Some of the top things they must do are support it's citizens, help create jobs, keep them safe from outside people, keep them safe from internal issues, and provide stability. All of these things are extremely important.
No, a government's primary focus should not be job creation for its people, because a government cannot truly create jobs. The government could hand each citizens a plastic spoon and have them farm by hand, but have they truly created jobs? All the government can do is enforce private property rights so that citizens, pursuing their own interests, can help each other through the invisible hand.