Shares in Caterpillar (NYSE:CAT) got a substantial lift Tuesday on expectations that China’s government will unleash a sizeable stimulus package to counteract the nation’s slowing economy.

It’s about time.

A cornerstone of the case for Caterpillar as one of InvestorPlace’s Ten Best Stocks for 2012 is that it’s finely attuned to global growth — and China is the engine of that growth. But the emerging-market behemoths of China, Brazil and India have all cooled down, disproportionately slamming Caterpillar’s shares.

The world’s biggest maker of construction and mining equipment saw its stock gain as much as 28% at one point in 2012 — but it has since given up just about everything. Shares in the Dow component are now up less than 2% for the year to date, trailing the S&P 500 Index by about 4 percentage points.

That sell-off has been humbling for Caterpillar bulls. A big part of my argument for Caterpillar heading into the new year was that fear over a China slowdown was already more than baked into the stock. Heck, China (and Brazil, for that matter) needed to tap on the economic breaks to curb inflation and take the the air out of its real estate bubbles.

But the world’s second-largest economy hit the brakes a bit too hard — and lower exports to recession-plagued Europe are also taking a toll. Instead of bringing GDP down from double-digit growth, to about 8.5%, China’s economy could slip below 8% growth this year.

Oops.

So it’s a relief that China is expected to start priming the fiscal pump. The government’s stimulus program could be as much as $315 billion, according to analysts at Credit Suisse. That’s about half the size of the package unleashed in 2008 in response to the global slowdown ignited by the financial crisis.

That’s still a big program — and remember that in China’s controlled economy, investment spending is unusually potent, since it flows from state-run banks to state-run companies. Furthermore, the central bank could cut banks’ reserve requirements or reduce rates to further stimulate lending.

That’s great news for Caterpillar investors, because if China picks up steam again in the back half of the year, Caterpillar is well-positioned to benefit. For its most recent quarter, CAT logged record earnings and a record order backlog — and that was in spite of the sluggish global economy.

Yes, Brazil and China acted as a drag, but other emerging markets remained robust. So did the need for replacement products in Europe even as the Continent struggled with recession. In the U.S., domestic growth in replacement demand for products more than offset the slowdown in China and Brazil.

China has been the big overhang on Caterpillar this year. Everything else is pretty much working. So the Middle Kingdom’s stimulus package should be just the catalyst Caterpillar’s stock needs to enjoy a strong second half of 2012.