The economy is not a zero sum game with a fixed number of jobs available. If it were, then restricting immigration or at least the access immigrants have to jobs would unambiguously benefit domestic workers. However, H1B immigrants, in particular, are frequently skilled workers that increase the productivity of the companies they work for, creating additional job opportunities, some of which are filled by domestic workers.
The direct effect of H1B workers is to drive down the wages and opportunities for domestic workers they compete with directly, but the indirect effect is the creation of complementary jobs, which may be skilled or unskilled. Similarly, increased immigration by low-skill workers drives down wages of competing low-skill domestic workers but increases the productivity of the economy, creating jobs (and goods/services) for skilled and unskilled workers.
A flow of new labor will benefit some domestic workers and harm others, irrespective of the current state of unemployment. Immigration is a political decision, and like other political decisions is made with an eye to who benefits from it and how influential they are on the political process, rather than a more abstract notion of what is good for "the country" or "unemployment." In other words, since some domestic workers are harmed by immigration and others are helped, you must define "good" before you can say whether H1B or any other type of immigration is good for the economy or its workers. The definition politicians use is "good for re-election," and since they have different constituencies, they disagree with each other on whether H1B or any immigration is good.
