If I Feel It Strongly, It Must Be True

Confirmation Bias?

It's called emotional reasoning.
Besides the wikipedia definition, another one is "Assuming that our feelings accurately reflect reality".

EDIT: There's also (not exactly emotional reasoning but similar) appeal to intuition - more like it is in the second version (check the logical form part) where it says
"Person 1 has a gut feeling about claim X.
 Therefore, claim X is true."

Regarding Peggy Noonan, I would say this is more of a case of psychological projection and Tu Quoque Whataboutism.  I've rarely read anything she's written that's not predictably False balance or bothsidesism. Most of her arguments seem pointedly targeted to deflect criticism from her very (Roman Catholic) Conservative ideology.

If we look at the difference between Cognitive Bias and Logical Fallacy, it only becomes a fallacy when we use it in an argument. The way the OP question is framed it is decidedly a Cognitive Bias. 

"Cognitive biases are our built-in patterns of thinking and affect how we interpret and process information from the world around us, and logical fallacies are errors or tricks of thought committed in an argument and they relate to how we construct arguments and communicate ideas to others."

This is simple subjectivism: I want "it" to be true, therefore "it" is true. Somewhat more in depth is to say it is the old rivalry between the Primary of Consciousness or Primary of Existence philosophies. The former falls of its own weight, but is nonetheless quite popular with religionists and flower children.