Dear Earl Roberts;
Thank you for your query--In the Centennial Edition of the Patriot Index, Part One, page 478, there are two Robert Campbell listings:
1) Robert b c (circa ) 1725 NJ; d 1796 NJ; m Mary Ayres; Pvt NJ
2) Robert b 1-20-1755 NJ; d 12-1-1831 PA; m Mary reynolds ;Pvt NJ Pnsr (pensioner)Neither one seems to fit with your robert campbell, but this does not mean he was not a Patriot--it just means that no one had submitted an application using a Robert who died in 1778 as you submited.
You can order a copy of pension records from http://www.nara.gov/
or Order forms for Military Service and Family History Records (Research Room, National Archives and Records Administration. There may be a branchof the National Archives in your area-- or in DC. The pension records may give more information on your Robert Campbell.
There are three George Campbell listings in the patriot Index but none show service in NJ however.
Stryker has written a book listing men of New Jersey who were in the Revolutinary War--and he lists them alphabetically by officers and regular enlistees--this may help you-- and with the help of the National archives, using that web site, you may find more information.
This is a free look up service provided by DAR Volunteers at the DAR message board. Good searching .