According to Keynesian economics the government can very much influence the economy. Government spending, Private domestic investment, personal consumption expenditures, and net exports are all factors that make up our economy's aggregate demand curve. The government can alter the levels of investment by raising or lowering interest rates. It can affect consumption by raising or lowering taxes. It can increase or decrease government spending, and it can certainly change the nations exports/imports.
The aggregate demand curve significantly affects our nations output and employment level, and increasing it can make a noticeable change. Unfortunately our level of debt is so high right now, beyond any reasonable amount I'd say, that it messed everything up and I would definitely not suggest increasing government spending as a method of increasing aggregate demand right now. At the same time, we need to reel that debt in, so how can we decrease taxes?
Note that a lot of people disagree with Keynesian economics, and unfortunately it's all that I know right now. So if anyone knows another type and can tear this ideology apart please do I wanna hear it