I believe this solves  mystery of who was Deborah's husband.  I would like opinions on this theory.
There were two different Reuben Elmores in Robertson County, Tennessee 
Below is the 1840 census record for Reuben H. Elmore,
and links to the other Reuben Elmore's.

For an informative article click on "Why U can't Find your Ancestors." then scroll down to "The Great Hang-up: Spelling of Names"

Click here to see a Reuben Elmore in the 1820 Census living close to a John Allen   could this be Deborah's father???  Ideas to investigate.....
Click here to see Reuben Elmore in the 1830 Robertson Co., Tennessee Census
 
This is Reuben H. Elmore listed in the Robertson County Census in 1840.  I believe he couldn't be found earlier  because Elmore was typewritten   Elmon in the census index. ( Ancestry.com now has this individual listed as Reuben H. Elmore --- see insert below.)  See the original writing, by the census taker, below.   It is obviously "Elmore." <<click this link to see handwriting samples to support this.
Name:   Reuben H, Elmore
Township:   Not Stated
County:   Robertson
State:   Tennessee
Roll:   533
Page:   152
Above is a copy of the 1840 Census heading  to compare with the original information below.  Notice: It doesn't line up!
 
This Reuben H. Elmore had 3 males under 5 in 1840 (possibly John A. Elmore and Reuben Harrison Clinton Elmore).   Since they were 13 and 15 ten years later in the 1850 census.. (notice: I changed this to 3 males under 5 in 1840 because when I went back and totaled the column, the census taker counted this as three. I first thought it was two.)    Actually, the extra male under 5 could belong to the female in the 40-50 age range or see speculations  in right-hand table below:
 Reuben was in the 30-40 age range in 1840.  There was one female in the 5-10 age range, one in the 10-15 age range, one in the 15-20, one in the 30-40 (Deborah??  If she were born around 1804 this would seem to fit???) and one in the 40-50 age group.        We need to find a will for this Reuben H. Elmore.   He was no longer in the picture in 1850.
Click here to see the names and ages of the sisters of John A. Elmore and Reuben Harrison Clinton Elmore (Deborah's family) and they fit into this census record (correct ages for this family! ).  This information provided by Joseph Lutes, descendant of Elizabeth Elmore Warren, daughter of Deborah.
A well thought-out response:  Thanks!

Sam & Twyla Harrison writes: 

I believe the Reuben H. Elmore you found is a real strong possibility of
being Deborah's husband. The age ranges seem to fit with what we know about the family so far.

As you pointed out the two young males under five would be a fit for John Allen and R.H.C.   Also, the female age 10-15 would be a fit for Lavinia Elmore Appleton, b. in 1828.   Deborah would fit as the female in the 30-40 range.   That leaves us with the younger females, one who was 5-10 and one 15-20.   They very well could have married and been out of Deborah's household by 1850.   The female who was 40-50 was probably someone else living in the household in 1840.  

The use of the name Reuben among Deborah's known children would lend strong support to her husband being named Reuben.  John Allen named a son John Reuben.   R.H.C. himself was named Reuben.   Lavinia named a son Reuben Harrison Clinton.   Is it possible that Reuben H. Elmore's middle name was Harrison??   Was Deborah's maiden name Clinton??  Did Lavinia name her son ( Reuben Harrison Clinton Appleton) after both her father and mother? 

Some other speculations re: Reuben H. Elmore and the connection to Deborah from Twyla Harrison:
    - 3 boys under 5.  In those times there was a high death rate among young children and babies. It would not be unusual that one of the young boys died.  Or, as you suggested, he could be the child of the older female in the household.
    - 1 female age 5-10.  If indeed Elizabeth Warren were Deborah's daughter, she could fit here.  Elizabeth was 40 in the 1870 census, so she would have been born about 1830, and thus would have been about 10 in 1840.
    - 1 female age 40-50.  She is probably too young to be the mother of either the parents in this household.  It could be an older sister of either of them.
    - finally, perhaps the figure really is a 2 in the "under 5" and the census taker totaled wrong.
 Thanks Twyla, input is critical for success in genealogy. 
 
 
Click here to see the 1850 census for Reuben Elmore
(obviously a different person)
Click here to see a Reuben Elmore in the 1790 N.C. Wayne County