What can and should be done to create and protect jobs? This is one of many questions for which economists and the general public do not see eye-to-eye. The public is often misinformed, but economists can be cavalier in their dismissal of the public's concerns and priorities.
So what about all these people whose jobs are threatened if the government doesn't do something to protect them? There are lots of different reasons for unemployment and different ways to combat it, and there is plenty of reasonable debate in both areas. Let's just consider the rubber case specifically. In response to concerns about American jobs involving rubber, an economist would typically say that fewer American resources should be devoted to rubber, since up to a point we're better off buying it from the Chinese, and these resources will naturally find their way to other productive uses. Even if we can agree about the factual elements of this response, one might feel that the original question--what about the people whose jobs are threatened?--has not been addressed. The problem is that the redeployment of resources is a long-run phenomenon, but unemployment is an immediate concern. It can take a long time for these adjustments to happen, and it is unrealistic (as well as terribly unkind) to disregard the costs incurred along the way, including the harm to the material and psychological well-being of the unemployed.
In short, the public tends not to understand the long-run benefits of free trade, but the economics profession tends not to pay much attention to the (sometimes painful) transitions the economy goes through.
In my opinion, if the government does anything about the unemployed US rubber workers, it should help to ease their transition, which could be accomplished through a combination of unemployment insurance and retraining. This kind of thing already happens, through programs like Trade Adjustment Assistance, but I would say that it should be implemented on a far larger scale. Support for free trade is predicated on the potential for large gains. If spending some of those gains makes it more politically feasible to achieve free trade, it is worth doing. Instead of standing on the standard efficiency argument, we can make a far more compelling case to the public by easing the pain that free trade causes to some without sacrificing long-term efficiency.
More generally, focusing on job creation per se tends to miss the point. There will be lots of good jobs available if there is a lot of economic activity taking place. Creating jobs by doing anything other than encouraging the associated economic activity is counterproductive. When unemployed workers are retrained, they are more productive and thus more valuable to an employer, and that is why they can more easily be employed. No one would suggest that we should create jobs by mandating that construction companies can only use hand tools. Protecting jobs by restricting trade is a similar act of shooting ourselves in the foot.