Embargos are a (light-weight) act of war. And like most acts of war, they hurt the civilian population more than they hurt the leadership.
Protectionist trade policies to attempt to balance a huge trade deficit is just economic policy. Free trade is all well and good when both partners are trading freely, but China is not doing that. China uses forced-low labor costs, low quality standards, low environmental standards, and import quotas to ensure they come out way ahead on the balance of trade. This hurts US businesses who can't compete with Chinese companies prices because they have to adhere to much higher standards/costs.
Simply adding tariffs to Chinese imports wouldn't be enough though; while that would bring some money into the US budget, it probably wouldn't help US businesses start up to pick up the slack in imports, and US consumers would wind up footing the bill. We'd also need a reduction in taxes on businesses that produce the sort of products we import from China so we can kickstart US production. The lower taxes should lead to more US jobs and lower prices on the products, and the government shouldn't lose revenue because it'll be getting the extra tariff money. (It'll be a long time before US businesses can produce the volume of goods we import from China, even with tariffs and tax breaks in place.)