My mom's got a '94 Pontiac Grand Prix with a 3.1l V6 (which, fortunately, she'll be getting rid of soon). A problem just cropped up today. When it's started after sitting for a while, it'll crank, fire, rev up some (like it normally does) and then shut down. On a re-start, it starts fine and keeps going. The car doesn't seem to be lacking for power, and there isn't a misfire or anything like that.

I'm guessing fuel pump...I can hear it whining, but maybe it's on its way out. Any thoughts?

Thanks in advance!

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2001 VW Jetta TDI, 5 speed, daily driver
1991 Ford F-350, work in progress
1984 Ford F-250 4x4, 6.9l turbo diesel, 5 speed manual
Previous oilburners: 1980 IH Scout, 1984 E-350, 1985 M-B 300D, 1979 M-B 300SD, 1983 M-B 300D
Spark-free since 1999