Yes! According to this report in the NY Times at least. Here’s a couple quotes:
Today, six in 10 Americans say immigrants “strengthen our country because of their hard work and talents,” according to the results, while roughly three in 10 say immigrants are a burden “because they take jobs, housing and health care.” In a survey in 2010 with the same questions but different participants, Americans were almost evenly divided, with 45 percent saying immigrants helped the country and 43 percent calling them a burden.
and this too:
The poll is based on interviews with a random sample of 1,538 Americans who took the same survey last year. Support has remained “remarkably steady,” the survey found, for a path to citizenship for more than 11 million illegal immigrants in the country “if they meet certain requirements,” declining one percentage point from 63 percent a year ago.
The poll found that 17 percent of Americans favor legal permanent-resident status, but not citizenship, for those immigrants, while 19 percent favor identifying and deporting them. Those figures have also changed little from last year.
The article also notes that the Tea Party is a huge outlier from these numbers (in the anti-immigrant direction).