The best thing that a President can do to help the economy is give the press something else to talk about besides the economy. Economics boils down to applied psychology: when people think the economy is bad, they cut back on spending and investing. The media picks up on this and continues to talk about how bad the economy is. And consumers continue to avoid spending, and investors continue to avoid investing, and the media talks about that, continuing on in a viscous cycle.
To break the cycle, the media needs something else to talk about. The reason why the economy was so great during the 90's is because Bill Clinton accidentally gave the media all sorts of things to talk about. Bush had a recession that went away after 9/11. But a new recession started when people got bored with the War on Terror.
I call this the Zaphod Effect. Zaphod Beeblebrox was the President of the Galaxy in Hitchhiker's Guide to the Galaxy. His sole responsibility was to distract the public.
Many economists will insist that the Zaphod Effect isn't real. This is because the only time anyone pays attention to them is when the economy is bad. And for the Zaphod Effect to work, we have to ignore them.