Rep. Chris Shays [R-CT] sent questionnaires to his constituents and got over 24,000 responses. Some of the results are discussed here:

His question #23. Do you support deportation of illegal aliens?

Answers: Yes 70.5%, Not sure 14.7%, No 13.3%, n/a 1.5%

24. Do you support amnesty for illegal aliens?

Answers: No 60.3%, Not sure 20.9%, Yes 17.0%, n/a 1.8%

...28. Illegal aliens should be entitled to public health services.

Answers: Strongly disagree 49.4%, Somewhat disagree 18.8%, Somewhat agree 17.4%, Strongly agree 9%, No opinion 4.2%, n/a 1.2%

29. Illegal aliens should be entitled to public education and access to higher-education benefits.

Answers: Strongly disagree 56.1%, Somewhat disagree 17.7%, Somewhat agree 13.3%, Strongly agree 7.8%, No opinion 3.8%, n/a 1.3%

You can download the results in this 800k PDF file.

On the downside, "Immigration" only got 5.6% of votes for the third-most important issue for Congress to address.

However, the results above and some of the other results might give our favorite Mayberry Machiavelli pause. Most of the responses to the other questions show that these constituents seem much more likely to be Bush voters rather than, for instance, Kerry or Dean voters.

For instance, "Would you have voted to support the use of force in Iraq?" got support from 53% vs. 36%. A similar question involving Afghanistan was 75% in favor, 15% against. I'll leave a deeper analysis to others.