It seems to be relatively recent. The earliest citations I can find are:
Stolberg, Sheryl Gay, “Senate’s Vote-a-Rama: 80 in 3 Days,” NY Times, 27 Mar 2003, A20. “They were holed up in the Senate chamber for what they call Vote-a-Rama. Like the cherry blossoms, Vote-a-Rama, seemingly endless back-to-back votes on the budget, comes to Washington each spring, the budget season in the Senate.”
Akers, Mary Ann and Paul Kane, “In The Loop,” Washington Post, 20 Mar 2008, A13: “Vote-a-Rama Record? Senators and staff are still recovering from the record-setting blizzard of votes held last Thursday as part of the annual tradition known as ‘vote-a-rama’: the series of amendments on the budget resolution that are voted on consecutively.”
Clearly, the term was in oral use before these citations.
The OED has this for a first citation for -orama, comb. form:
1954 Amer. Speech 29 157 Audiorama, a display of acoustic instruments;..striporama, a burlesque movie.