The private sector is not always capable of looking at the big picture. In a capitalist society such as ours, each business will solely be looking out for it's own best interests, as success is generally measured by how much money is amassed. At times, this will cause the economy to to take a turn for the worst. For example, the cost of living has increased as property owners and businesses are trying to maximize profits in their are, but those who make minimum wage are left unable to support themselves, let alone any family they may have. In times like these, it's the governments duty to step in and raise a minimum wage. Businesses can't succeed if their customers can't afford to buy any products, and governments can't thrive if their constituents are too hungry to vote. By shifting government fiscal policy to free up some money for the lower and middle classes, the economy can be extremely stimulated.
No, the government is not generally capable of stimulating the economy, because the government cannot make or produce wealth. The government can only take things that other people have produced and redistribute them. When the government tries to make something, it is always inevitable inefficient. The government can only get out of the way for the free market.