FORTUNE — The management of General Motors Co. must be among those most ecstatic that the 2012 presidential election is finally over. The automaker’s ties to the U.S., a legacy of its 2009 government-supervised bankruptcy, soon could be no more.

With presidential politics resolved, the administration has little reason not to sell its 25% stake in GM (GM), thereby removing the Government Motors nickname so annoying to many of the company’s executives. But the end of election season is bringing GM another reason for cheer: the company is closer to introducing the latest version of its full-size Silverado pickup truck.

Neither GM nor the government is saying when a share sale may take place. But last week the automaker secured an $11 billion line of credit, raising its available cash and credit to $42 billion. With GM’s balance sheet flush, the government has the flexibility to sell the shares gradually, sell them all at once to the public or to GM. It could, of course, also stand pat.

MORE: In Detroit, a tale of two CEOs

The new Silverado, a top profitmaker for GM, will be shown to the press in Detroit on December 13. Michelle Krebs of Edmunds.com calls GM’s timing with the vehicle “fortuitous,” given a recent uptick in construction activity in the U.S. Pickups are used widely by construction trades, which postpone replacing vehicles when activity declines. “The question will be whether GM made enough changes on its truck,” she said, to match Ford’s (F) latest F150 and Chrysler’s latest Dodge Ram models. Ford is featuring what it calls an EcoBoost engine, which uses turbo-charging technology to improve mileage and power output.

The current Silverado, which also is sold by GM as a GMC Sierra, was introduced in 2006. GM, as is its custom, isn’t saying much about the new model in order to build suspense. But power and fuel efficiency are especially important to commercial owners, so GM has revealed that the new model features a “new generation” of engine with cylinder deactivation in certain conditions that saves fuel, according to Tom Wilkinson, a GM spokesperson. In a statement Wilkinson said “the recovery of agriculture and energy has been good for the pickup truck market, and if housing does gain momentum next year, it could prove to be a good year to launch a new light-duty pickup,” meaning the Silverado.

Through October, Ford has sold more than 520,000 F Series pickups this year, a gain of almost 11% from a year ago. The Dodge Ram sold almost 239,000 in the same period, a gain of about 20%. The current model of Chevrolet Silverado, meanwhile, sold 336,500, a scant 1.3% improvement from last year.

MORE: How GM learned to love the small car

One of the reasons pickups are relatively profitable is that the market is large and has faced relatively little competition from foreign manufacturers, compared to family sedans, SUVs and luxury cars. For GM, which offers an entire range of pickup sizes, towing and hauling capacities, the vehicle category constitutes “the family jewels,” in financial value. GM’s new pickup platform and design themes also serve as the basis for the Yukon, Suburban and other fullsize sport-utility vehicles. Like the pickups, they are quite profitable compared to cars, and a key determinant of GM’s bottom line.

GM is a global automaker that remains a work in progress, battling to establish its independence from government control. That independence may ultimately be easier to assert and reinforce with the strong earnings that a popular pickup truck line may generate.