Miller, 68, was not yet a year into a new four-year term, which he won last year by more than 5,700 votes.
A spokeswoman for McAuliffe said Monday that the governor had not turned his attention yet to calling a special election.
The state constitution leaves it to the governor to call for this election, and state law sets out various windows when the election is allowed.
It must be held on a Tuesday, and it cannot be held within 55 days prior to a primary election or general election. Nor can it be held the same day as a primary, which means the June 14 congressional primary date is not an option.
Neither is the May 3 city and town election date. The Nov. 8 general election seems the likeliest candidate.
Miller represented District 1 in the Virginia Senate, and the district includes parts of Newport News, James City County, Williamsburg, Hampton, York County and Suffolk. Nearly 70 percent of its population is in Newport News.
The district leans decidedly Democratic. U.S. Sen. Mark Warner won 57 percent of the 1st during his 2014 re-election race. McAuliffe won 55 percent in 2013 and President Barack Obama won 59 percent in his 2012 re-election campaign.
Fain can be reached by phone at 757-525-1759.