The truth is yes. And no. A strong dollar is good for some sectors and not as good for others. The answer to this question varies greatly with your position. When the dollar is strong it means that you can buy more foreign currency for your money. If you are a person looking to enter the Forex market, that could be great. If you are a trader who holds large positions of foreign currency it would be bad for your portfolio. This is just one example of how a strong dollar can be both good and bad.
One situation where a strong dollar is a positive thing is when travelling abroad. The travel is cheaper, you can purchase more currency, so your buying power is higher. In the US it means that a consumer who buys imported goods can get more for his or her money but a consumer who is selling exported goods does not do as well. For example, most luxury cars are imported so they will be less expensive when the dollar is strong. If prices of imports fall, there is more disposable income in the wallets of most Americans. This leads to a higher standard of living for many Americans which is indicative of a good economy.
Sometimes, whether or not a strong dollar is good for the economy depends on the reason that the dollar is strong. If the dollar is strong because other currencies have weakened that is a different story than if the dollar is strong because of competition and increased international trade.
In terms of the job market, unfortunately, when export business is slow, so is the job market in the US. That when the dollar is strong, exports do not sell as well, then the companies who do most or all of their business in export suffer and they do not have jobs to offer. Fewer jobs leads to a decline in the economy because obviously, those without jobs have less money to spend.
The flip side of the travel aspect is that although travel outside of the US is less expensive, travel to the US becomes more expensive, thus lowering the number of tourists and what they spend. Tourists to the US account for a percentage of the spending locally. Therefore, when the dollar is strong and the cost of travel to the US is high and the money that the tourists have to spend buys fewer things, they spend less and the US economy suffers somewhat.
In addition, another negative to the strong dollar is that companies who have international sales or franchises will see their profits reduced and that will affect their businesses and their investors. This can be mostly seen in larger corporations such as McDonalds, Coca-Cola, and others who have the majority of their sales in other countries.
So, as you see, the answer to whether or not a strong US dollar is good for the US economy really depends on who you ask. There is no one clear answer.