Here is what I have on your line- perhaps it will help. I cannot prove Nelson was a son of Jeremiah BUT hopefully this gives you some clues to advance your search. The LeValley connection may help.
"From Paul LeValley: "Here is everything I have on Lydia LeValley who married Nelson Bresee. She was born June 16, 1820 m. June 13, 1836 Nelson Bresee (s. Jeremiah, b. 6/18/18__ 11? Davenport NY).
He m. (2) 3/25/1869 Mary E. Briggs in Knox Co. IL d. Oct. 1, 1868 bur. Henderson IL cem. with young son and daughter Her tombstone elaborately gives his and her exact birthdates, marriage date, and her death date. Since his death inscription is blank, he probably is not buried with her.
1840 Census: Delaware Co. NY BRESEE Pg 418 - Nelson: 1 m 20-29; 2 f 0-4; 1 f 20-29. (living next to these Bresee's- John C. age 30-39; Christopher age 20-29; Christopher I household with a female 40-49 and son 15-19)
1850: Knox Co. IL Hendersonville Pg 396 HH 1033-1159, BREESE- Nelson 32 Carpenter $500 NY; Lydia 27 NY; Juliett 14 NY; Ira 8 NY; Florell 4 IL; Celstia 1/12 IL. (Reflects they moved from NY to IL between 1842 and 1846.)
1880: Nelson BRESEE is in home of his son Ira--- Rohnerville, Humboldt, California,Film 1254066 ,NA Film No.T9-0066, Pg 410C - BRESEE Ira D. 38 NY NYNY, farmer;Mary E. Wife22KS KYPA;Leonard 5CA NY PA;Fred 3 CA NYPA; Maude 2 CA NY PA;Nelson BRESEE, Father, 69 NY Carpenter NYNY; Daniel EAST,Other, 22AUSTRALIA Farm Laborer ENGIRE. This shows Ira moved to CA by 1875. "