For example, Hillary Clinton said on the campaign trail that she would have put Bill in charge of fixing the economy, because he knows how to do that. Presumably he "knows how" because he presided over one of the largest and most impactful periods of economic growth in the country's history. And indeed, we owe a large debt of gratitude to Bill Clinton for going around the country personally starting the internet startups that fueled dot com boom of the '90s after he had Al Gore invent the internet.
So what Hillary is suggesting there is that Bill has another world-changing technology up his sleeve that would drive business for decades to come, which he would have unveiled had she become president. Honestly, it seems pretty selfish of them not to share it even though they lost.
Contrary to what chart-making Democrats would have you believe, a study by Alan Blinder and Mark Watson, economists at Princeton University, found that the president has as much to do with economic growth as your personality has to do with winning The Bachelor -- that is to say, maybe a bit, but it's debatable. After they controlled for factors like the price of oil and changing demographics, they found that it didn't matter whether the guy in the captain's chair was wearing a blue or a red tie. That means that every four years, we engage in a collective act of pointless masochism by having our presidential candidates bore us with nonsense about how they'd improve the economy. It would be just as effective for a debate moderator to say, "And now for our section on the economy, both of you shut up because nothing you say matters," and then sit there for 40 minutes in blissful silence.
One reason party doesn't make a huge difference is that economists often don't fall neatly along party lines. An economic adviser to John McCain was very much in favor of an economic stimulus, and even complained that Obama's eventual stimulus wasn't big enough. The chair of the Federal Reserve usually serves long enough to work with presidents from both parties, and often doesn't act in a "liberal" or "conservative" way based on who appointed them. Contrary to Air Force One, rare are the situations in which the president has to go rogue and solve problems single-fistedly.
Another thing to keep in mind is that any impact presidents do have is on a delay much longer than our current 24-second news cycle. You don't invest in infrastructure by going loading up a T-shirt cannon with cash and yelling "Build roads, jerks!" as you fire indiscriminately from the roof of the Capitol. Who thinks that government spending works that way?
And speaking of Trump, it is worth noting that, while presidents haven't generally had a large immediate impact on the economy, it's not that they can't. Nixon famously instituted a freeze on all prices and wages in the United States, which was quickly proven to be a very stupid thing to do, and it took years to undo. If U.S. companies can't import talented workers from other countries because of extreme immigration laws, that would be problematic. The Iraq War spiked the price of oil, which was immediately bad for the economy. Attorney General Jeff Sessions announced that he thinks the problem with the drug war was ... apparently nothing, as he wants to keep fighting that war the same old way, locking up millions of people -- which certainly has an impact on our economy the moment someone's put away for having a joint. In a perfect microcosm of how the entire world works, a president can definitely fuck things up, but their "surefire" plan to make things go well is just so much hot air.