The government's money comes from the people of the whole nation. If the government pays, it is using money from millions of individual people.
Another question might be if only road users should pay for the road system (through tolls etc.), or some certain other sub-set of people in the nation.
Roads cost money. All money ultimately comes from individuals (even if it is through the government). As it is unavoidable that individuals will ultimately have to pay for roads, the question then is: which of those people will have to pay (all or only some)?