Google‘s cross-platform advertising strategy is looking pretty miserable right now.

Led until recently by former Google U.S. sales executive Tim Armstrong, this strategy sought to spread Google’s influence beyond search advertising to include print ads, radio ads and TV commercials. (See our past coverage of those initiatives here and here.)

Now, unconfirmed reports are emerging that Google’s cross-media ad operations didn’t perform as well as expected in the first quarter.

Layoffs across its sales operations are mounting, and many of its efforts have produced embarrassing results. Even in its last bastion of hope, TV, where Google seems to have better traction, more advertisers are moving their dollars elsewhere. Yesterday, Reckitt-Benckiser became the latest agency to move ad dollars to online video from TV, shifting $20 million to the web. Finally, powerful ad agencies, long skeptical that Google is trying to cut them out of the ad placement business, have continued to stymie its efforts.

Armstrong remains highly respected by his peers in the ad industry, and within Google too, with most saying he was well liked. But it’s increasingly clear that he was out of place at Google. It’s hard to lead a sales organization in a culture that relies on engineering-led approaches. It’s now obvious why Armstrong, who embodied Google’s vision to take over other non-search advertising industries, felt the lure to leave and take the helm at AOL, announced two weeks ago. The job was no longer fun. And Google could no longer retain him through promotions — so it simply placated him, letting him invest in companies like Patch and Associated Content through his own investment group, Polar Capital Group, something the search giant tolerates for only its favored executives. The writing was on the wall. AOL will be a challenge too, but at least Armstrong will start with a blank slate.

A year or two ago, Google’s bold, sweeping advertising strategy seemed to be written in the stars: It was on a roll, and there was no stopping its algorithmic rigor from vanquishing old-economy advertising and industry titans. It was simply more efficient. But one by one, Google’s efforts proved much tougher than the company anticipated, and the economic contraction has only made things worse.

Surprisingly, we’re hearing Google’s print initiative was actually profitable before it was shut down — but not by much. And TV was on target to be profitable in 2009, but again, the surge in clients it had hoped for didn’t materialize (the TV Ads team has come under fire for working with only a few hundred clients at a time and retaining few). Now Google insiders are realizing their vision for a grand advertising strategy will take a lot longer — unfolding over the next decade or two, perhaps. Some say that was the idea all along and that the company just got ahead of itself.

Aside from radio, TV and print, Armstrong also oversaw strategy around properties such as DoubleClick DART, Google’s ad serving technology that places ads on high-end publishing sites. That unit began laying people off last year (although that might have been due to redundancies following DoubleClick’s acquisition).

Google increased its market share in display ads over the past year, but that growth came at a cost. Google has spent roughly $10 billion on non-search initiatives and properties, with much of it being written off, we’re told. The $1.6 billion YouTube deal, for example, was under Armstrong’s jurisdiction. Word is that some employees at the video site are only staying through the summer to fully vest their options but will then leave, with YouTube still allegedly losing $200 million a quarter on streaming costs. Google has not responded to requests for comments on this article. AOL declined comment.

To date, YouTube has only signed a small number of full-length content deals with companies like CBS Corp.; for the most part, it’s struggling because most other advertisers are still only experimenting on YouTube with small budgets, if at all. Last week, Google announced it would start letting advertisers purchase YouTube ads through its Google TV Ads platform. But considering the shaky state of both, that’s a lot like patching a leaky boat by stacking it in another one.

Throw in the almost $1 billion Armstrong arranged for advertising on MySpace — which executives have already acknowledged yielded “disappointing” results — and you see why the search giant might be getting concerned.

Another problem is that many internet companies compete against Google — or are anxious about Google’s agenda — and want to promote their own services and ad-selling platforms. Take Google’s DART ad-serving technology. It targets the top 200 publishers, seeking to serve high-priced ads. These top 20 or so publishers account for half of the DART unit’s revenue, but they are hurting in the downturn, and many don’t want to use the service anymore. Yahoo, the largest online publisher, but a fierce competitor to Google, doesn’t use it. AOL, another large publisher, doesn’t use it on its own higher-end properties. Microsoft, the No. 3 publisher, owns its own ad-serving technology, Atlas. And Viacom, another large publisher, recently announced its intention to move away from DART. Aside from that, the massive ad agencies that control the real dollars, lack trust in Google.

According to our sources, Armstrong was pretty competitive with Google’s ad sales executive in Europe, Nikesh Arora, who had the luxury of obsessively focusing on advertising initiatives that yielded real profits (Armstrong’s cross-media initiatives were only in North America). Arora would have nothing to do with radio and print, and for a while enjoyed a halo of success. When he took over European sales, the continent’s currencies rose against the dollar, helping his revenue appear larger than it actually was without him doing a damn thing. But with the decline of European currencies in recent months — the pound has depreciated 40 percent since the third quarter — his fortunes have changed. So, despite some unfounded speculation, it’s not like Armstrong was pushed out by Google management in favor of Arora, or anything like that.

Meanwhile, the sad tale of the newspaper, radio and TV divisions is pretty well known. Publishers in these industries prefer to do deals with established advertising agencies over golf. They don’t understand or care about Google’s algorithms. This realization urged Google to shutter its print and radio advertising units. And its ambitions for TV have also been scaled back. On Thursday, Google disclosed it was cutting its sales and marketing staff by nearly 200 positions, the company’s biggest round of layoffs not associated with a merger. Some of them have come from the TV division. It doesn’t bode well that Google fiercely denied the demise of its Audio Ads team mere weeks before it was disbanded. That means we can’t put a lot of stock in the company’s protests that TV Ads are here to stay.

It will be interesting to see if the decision to have Google TV Ads broker YouTube and other online video advertising will make a difference. At least there is some commonality between the format of TV and online. Arguably, tracking audience behavior will be more precise as more viewers move to watching digital TV — which is good for advertisers, but also good for Google, which can offer valuable tracking and measurement solutions to clients.

Regardless, it looks like Google overshot its bounds, a rare misstep for a company that once seemed invincible. Will the fissures continue to grow, making room for some of its more wiley competitors? Or will it quietly shut down the divisions that aren’t producing and act like nothing happened?

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