Recent grim economic news amounts to a test for companies regarding their workforces.

Will firms take a short-term, panicked approach, axing people and valuable programs to shore up earnings over the next several quarters? Or will they act according to a long-term vision, where they live up to claims of treating people as “their greatest asset” even at the expense of short-term profits?

The stakes are big, and could well determine which firms emerge as the places with the most employee engagement, the best ability to attract talent and the greatest sustainable performance.

Signs of a double-dip recession or protracted downturn include the June employment situation. U.S. job losses in June outpaced those in May, reversing several months of improving payroll job declines.

It’s hard to judge how employers have handled the economic troubles so far with respect to their people. On the one hand, there’s evidence firms rushed to cut employees—72 percent of firms surveyed by consulting firm Watson Wyatt Worldwide in April had laid off employees or otherwise reduced their workforce.

But there also are indications of sound responses. A May report from consulting firm Towers Perrin (which plans to merge with Watson Wyatt) found that 74 percent of employees agree their company’s structure facilitates efficient operations, up from 66 percent in the last quarter of 2008 and 58 percent in the first quarter of 2008, “suggesting the latest rounds of restructuring have been done thoughtfully and in a manner that doesn’t automatically demand doing more with less.” In addition, company interest in furloughs—which can preserve morale if used instead of a layoff—has grown.

Towers Perrin found that employee engagement globally held steady between the fourth quarter of 2007 and the first quarter of this year. But polling firm Gallup found a slight drop in engagement among U.S. workers between July 2008 and March 2009.

And the Corporate Executive Board research group found that the percentage of employees globally displaying high levels of discretionary effort dropped sharply between 2005 and the first quarter of 2009.

By now it’s pretty clear that engagement can be a key to company success, and a management model focused on engaged, involved employees seems likely to be the best bet for tomorrow’s fast-paced global economy.

In this light, trimming jobs from already lean firms is risky. Gallup has found that organizations with a layoff or downsizing saw the level of “actively disengaged” employees rise by 3 percentage points, to 24 percent.

It’s possible to avoid an engagement drop with a layoff, says Jim Harter, chief scientist for Gallup’s workplace management and well-being practice. Experts including Harter suggest management explain the rationale for any downsizing to employees.

Some companies may have to cut people in the coming weeks or months just to stay afloat. There are no easy answers in this ugly economy. But it may be time to suck it up and hold on to the employees that firms profess to value so highly. The long-term payoff—in engagement, in reputation and in performance—could be much bigger than the short-term pain.