Is it a common way to use “heartland” as in “give a heartland shout-out / comment to somebody”?

I found the phrase, “give a heartland shout-out to sb,” in the article of today’s (December 9) New York Times, titled “The Rough Rider and the Professor,” which comments on President Obama’s speech delivered in the Kansas high school gym on December 6th. It reads:

“Obama gave a heartland shout-out to Dwight D. Eisenhower, Warren Buffett and his own Kansan grandfather, who served in General Patton’s Army. It was a rhetorical device, to make common cause with men of common sense. This made it easier for him to make his main point.”

From the context of the sentence, I guess “a heartland shout-out” means a critical or very important shout-out.

But when I checked Oxford online dictionary, it defines “heartland” as:

1. the central or most important part of a country, area, or field of activity:e.g. wildlife sites in the heartland of Russia
2. The centre of support for a belief or movement e.g. the heartland of the rebel cause

Cambridge Dictionary simply defines ‘heartland’ as “the central or most important area.”

Merriam-Webster defines it as;

1. Central area: as a: a central land area.
2. The central geographical region of the United States in which mainstream or traditional values predominate.
3. A region where something (as an industry or activity) most strongly thrives.

Except definition of 2. of OED, none of the above definitions seems to me to sit very well with the “heartland shout-out”.

Is “give heartland shout-out (message, comment, advice, proposition)” a common usage of “heartland,” which comes top of mind to me as simply a geographical place or area.

Doesn’t it sound clumsy if I say to my friend or subordinate in a serious look, “Listen, I’m going to give you 'my heartland advice.'”?

Your feeling is correct that "The central geographical region of the United States in which mainstream or traditional values predominate" is the intended definition. In the quoted passage, a heartland shout-out is a shout-out which resonates with traditional American values and invokes "Americana" images and figures (here, Kansas, General Patton, a grandson honoring his grandfather, and so on).

Heartland shout-out (or message or advice or whatever) is certainly not a stock phrase. To me, the use of the word heartland here carries at least a certain playfulness, and at most a kind of gentle sarcasm, suggesting that American values were invoked in a stereotypical, over-the-top way.

Thus, to answer your question, this metaphorical usage of heartland (referring to the values/connotations, not the geographical region per se) is reasonably familiar and understandable to me as a native speaker, but it would not be used in the context of giving someone serious advice.

It is a deliberate play on words.

It tweaks the common: "a heartfelt [expression]" (where [expression] is a shout-out, a plea, or similar), substituting heartland for heartfelt.

That substitution has two nuances: one, that that shout-out may not be heartfelt at all. And secondly, that it was targetted at a particular stereotypical valueset associated with the voters of America's "heartland", a particular socially-conservative economically-liberal section of mainstream WASP middle-America.