NEW YORK — It sounds crazy: Just a week after the White House scolded Chrysler LLC for relying too much on gas guzzlers, the company is heading to a marquee auto show Wednesday to unveil a new SUV.

Chrysler insists the Jeep Grand Cherokee, which clocks in at 20 mpg in its two-wheel-drive version and 19 in four-wheel-drive, is a crowd favorite and a crucial part of its lineup.

"This is a very important vehicle for us. It's one of the primary legs of the Chrysler stool," Chrysler spokesman Rick Deneau said. "Customers have told us they want this vehicle and that it's the right size."

The 2011 model is 11 percent more fuel efficient than its predecessor, powered by a cleaner and more powerful engine. Still, Chrysler's decision to debut an SUV as its only new car at the New York International Auto Show seems like odd timing to say the least.

On March 30, the Obama administration issued a scathing rejection of the company's survival plan and gave it 30 days to secure a merger with another automaker, most likely Italy's Fiat SpA.

The White House slammed Chrysler for having a product lineup so heavily weighted with trucks and SUVs. It added that the automaker does not have enough products in the pipeline to meet an expected increase in demand for small cars.

But Chrysler is standing by the Grand Cherokee. It's profitable, recognizable and the No. 2-selling vehicle in the Jeep lineup. Grand Cherokee sales fell by almost half during the first three months of the year, but its market share has remained steady, according to Autodata Corp.

"It is one of their most important vehicles," said John Wolkonowicz, senior automotive analyst for the consulting firm IHS-Global Insight. "The market for SUVs has not completely gone away, particularly for smaller ones like the Grand Cherokee."

And Chrysler, which is clinging to a $4 billion taxpayer lifeline, has little choice but to focus on the present.

The automaker expects its tentative partnership with Fiat to plug the holes in its small-car offerings. It hopes fuel-efficient Fiat cars, like the two-seater 500, will sell on this side of the Atlantic.

But even if an alliance with Fiat goes through, the Italian automaker's vehicles wouldn't make it to the U.S. until 2011. That means that until then, Chrysler has little choice but to survive on revenue from its current vehicle lineup.

"I think it's going to be written up as being out of touch, but from a business standpoint, I think it's the right thing to be doing," Wolkonowicz said of the Jeep's unveiling.