I want to premise this argument by saying that my yes is a skeptical yes, to say the least. I am a non-partisan voter, and I believe that at certain times in our history, certain types of economic policies favored our country. It was not a matter of Democrat versus Republican, but rather a matter of what situation our country is currently in. With the current economy, there are certain Republican principles that can actual benefit economy (allowing small businesses to develop without federal spending, for example).
The Republican Party continues to pander to the rich, thanks in part to a bank bailout during the Bush administration and when the GOP put Mitt Romney front and center as the party's choice for president. Under no uncertain terms should Republicans, in their current state, be trusted with the economy.
The entire Republican presidential campaign had been based upon stonewalling and obstructing the president and hoping that they could make him look bad by not letting him get anything done. It was a very cynical strategy that was ultimately based on dishonesty. It was also one that failed, because Barack Obama was re-elected; I think that proves that most Americans don't trust the Republicans, either.
Matter of fact, I don't think the Democrats should either, they ALL are crooks and corrupted. Doesn't matter which side of the fence they're on, they all lie, they all cheat, and they all steal from the American public on a regular basis. So not only do I not think Republicans should be trusted with the economy, I don't think the government itself should be, because they have done little to gain my trust and everything to shake it.