There's a popular sweetgum cultivar that gets to about 3x60' called Slender Silouette

There are numerous narrow, columnar forms of various maples, as well as the Liquidambar mentioned previously. However, maintaining a spread of only 2 feet over the life of the tree is very unlikely -- all will expand with maturity to anywhere from 6-15', sometimes more.

FOUND COLUMNAR MAPLE 2-3 FOOT WIDE 60 FOOT TALL, CALLED ERECTUM, FROM COLONIAL NURSERY IN BLUE SPRINGS MISSOURI.TRYING TO LOCATE A GROWER, THERES ONE GROWING NOW IN FRONT YARD OF A HOUSE IN WARRENSBURG MISSOURI AT HOLDEN AND SOUTH STREET, GOGGLE MAP WORKS THERE.

The unusually narrow maple is 'Newton Sentry'. 'Erectum' is one of its synonyms. It has also been called 'Columnare', 'Sentry', and 'Monumentale' - but other maple cultivars have also been called by those last two names. Be sure to verify stock is the desired one before purchasing.

I doubt the columnar sweetgums on the market will remain as narrow as this, not even columnar Swedish aspen is as extreme in growth habit.

That's one narrow tree in Warrensburg. I've seen one as narrow but not as tall and growing in a lot of shade - Minnesota Landscape Arboretum. I know a nursery in Ontario that carries one of the narrow selections and ships to the States. Email me if you don't find anything and I'll give you the info. And it just dawned on me - there's a nursery on the West Coast that carries what they call Monumentale - Whitman Farms and they have a website.
Marshall

Have you really got a use for a tree this narrow? It seems like some nurseries order them once and can never get rid of them and they discount them heavily.
I'm curious to know how you found a use for them since they can look kind of silly planted in the open, imo and if the squeeze is that tight where you want to plant it such as in between homes then chances are the roots can be a problem with foundations.

For photos and descriptions of upright forms likely to be found on the market...

Here is a link that might be useful: JFS Introductions