A 2003 survey on a US nationally representative sample found that 71.3% of respondents agreed that
“It’s OK for immigrants to be loyal to both their home country and the U.S.” [statement that] was used to gauge Americans’ attitudes toward immigrants’ dual loyalty.
while the rest of 28.7% disagreed. Approximately 25% of the sample were non-respondents though, but that's not reflected in the aforementioned percentages, which only reflect those who answered the question.
As for demographic correlates of this attitude
three of the four variables in the social location cluster (gender, education, and income) were not significant in structuring nonimmigrant Americans’ attitudes toward immigrants’ dual loyalty; age was the only factor that had an effect. [...] older respondents were more likely to disagree with the statement. [...] those who resided in the Northwest and Midwest were less likely to disagree with the statement “It’s OK for immigrants to be loyal to both their home country and the U.S.” than were residents of the South and West. [...] political party affiliation was the single most important variable in structuring attitudes toward immigrants’ dual loyalty within the cultural and political boundary dimension. Those who identified as Republican were 1.63 times (60.3 percent) more likely to disagree with the idea of immigrants’ maintaining dual loyalty than were those who self-identified as Democrats or independents.
The correlation with age suggests that the US public attitude to the "dual loyalty" issue might have significantly changed over time. Are there any longitudinal surveys (i.e. same question asked at multiple points in time) on this matter?