Right wing website Newsmax held a poll in which they asked people how to reduce the deficit.

Below are the results (copied from here):

To close the federal deficit, Congress and the President should:

Raise taxes  85,099( 08%)
Cut spending 274,206( 27%)
Cut taxes and cut spending 593,479( 59%)
Raise taxes and increase spending 38,066( 03%)

Do you favor significant cuts to Medicare?

Yes, cut Medicare significantly 91,174( 09%)
No, don’t cut Medicare significantly 894,105( 90%)

Read more on Newsmax.com: SurveyResults. [Note from 2012/11/13: the Newsmax webpage no longer show the results above concerning Medicare.  But I found other webpages which mentioned the result:  here and here and here, for example. This suggests that Newmax removed the results because they didn’t like them. Instead, now they present the (counterfactual) question “Should Congress restore $500 billion in Medicare benefits for seniors that the Obama plan cut?”, for which 68% of respondents (961,924) said “Yes, restore the Medicare benefits.” Americans love Medicare.    See also Newsmax Uses Poll to Spread Lies.]

What’s significant is that that 86% of respondents (over 3/4 million people) wanted to lower the federal deficit by cutting taxes and/or spending and yet 90% of respondents (almost 900,000 people) oppose significant cuts to Medicare.

Also, 67% of respondents (965,774) said “No, don’t repeal it all to” in response to “Do you support the full repeal of President Obama’s healthcare plan Congress passed in 2010?”.