The Dust Bowl's causes, generally climatic due to drought in the Plains in the 1930's combined with a poor management of agriculture in these areas, lead to a mass migration of farmers from the Southern Plains to other parts of the country (think "Grapes of Wrath" from your high school reading).
Drought has been a big issue in the Plains and Midwest this year, with a large swath of real estate from Minnesota and the Dakotas south to Texas under extreme and exceptional drought conditions not unlike those felt in the 1930's.
the January-October period of 1934 was the driest on record nationally and 1936 was the 15th driest on record. This year's dry spell, while impressive, lacks the year to year persistence of the 1930's.
However, modern agriculture and a better understanding of the Plains' soil and climate may very well go a long way to prevent a full blown repeat of the magnitude of dust storms that ravaged the country nearly eighty years ago. There may certainly be dust storms on a regionalized basis but probably not as widespread to the point where dust blows into New York and Washington.