As far as the "leaning only slightly" public is concerned: From the Newsweek poll referenced in the original Huffington Post

"Who do you trust more to make decisions about U.S. policy in Iraq: President Bush or Democratic leaders in Congress?"

President Bush, Democratic Leaders:
Republicans: 74, 14
Democrats: 7, 87

"In general, do you favor or oppose President Bush's plan to increase the level of U.S. troops in Iraq by about 20,000?"

Favor, Oppose:
Republicans: 60, 21
Democrats: 7, 92

"Do you think Democrats in Congress should take action to try to block the additional funding needed to pay for the additional troops Bush wants, or should not try to block funding?"

Should, Should Not:

Republicans: 12, 77
Democrats: 67, 25

If these respondents (supposedly typical citizens, not political hacks) leaned any further they'd be horizontal.

You can also go to the Fox News survey, and look at similar responses by party line to various questions.

I like to think each individual arrived at their conclusions by reason and thoughtful analysis, but I doubt it. You might also note which party tends to be less monolithic in its opinions. Hint: it ain't the "party of diversity."