Conyers leads Michigan state Sen. Glenn Anderson (D) by 57 to 17 percent, according to the poll, with the other candidates in the race pulling single-digit support.

Some Detroit observers of the civil rights icon and 48-year congressman had expressed concern that he wasn't taking his primary in a newly redrawn district seriously enough — but if those numbers hold true on Tuesday it will signify that he was never in trouble in the first place.

In Detroit's other newly redrawn congressional district, Rep. Gary Peters (D-Mich.) has a big lead over fellow Rep. Hansen Clarke (D-Mich.), 52 to 33 percent. Peters has the backing of most of the city's powerful unions as well as much of its political establishment.

The two automated polls of 800 likely primary voters were conducted by EPIC-MRA on last Saturday and Sunday, and had margins of error of plus or minus 3.5 percentage points.