This new Center for Immigration Studies analysis suggests yes.
"A new analysis of government data shows that two-thirds of the net increase in employment since President Obama took office has gone to immigrant workers, primarily legal immigrants. Although the level of new immigration overall has fallen, legal immigration remains very high. While economists debate the extent to which immigrants displace natives, the new data make clear that there is no general labor shortage in the United States. This analysis calls into question the wisdom of bringing in more than a million new legal immigrants each year at a time when the employment situation remains bleak."
http://cis.org/who-got-jobs-during-obama-presidency
"A new analysis of government data shows that two-thirds of the net increase in employment since President Obama took office has gone to immigrant workers, primarily legal immigrants. Although the level of new immigration overall has fallen, legal immigration remains very high. While economists debate the extent to which immigrants displace natives, the new data make clear that there is no general labor shortage in the United States. This analysis calls into question the wisdom of bringing in more than a million new legal immigrants each year at a time when the employment situation remains bleak."
http://cis.org/who-got-jobs-during-obama-presidency