Here's what we know from the show itself:
-- Bartlet was preceded by a two-term centre-right Republican, under whom Leo served as Secretary of Labor
-- Two fictional former Presidents are named: D.W. Newman (one-term Democrat) and Owen Lassiter (two-term Republican).
-- The last real-world President to be named in the show is Richard Nixon
-- There were four Republican presidents between 1969 and 1999 altogether
-- Newman used the same Air Force One as Bartlet
-- Lassiter's former staffers & Cabinet secretaries at his funeral are very old.
The first and last point in particular leads me to believe that Lassiter was not Bartlet's immediate predecessor. Plus the fact that Lassiter is clearly meant as that universe's cultural equivalent of Reagan, and serving 1991-1999 is too late.
So, here's the idea: TWW-universe election law is a little different than ours, in that the ascension of the Speaker of the House or lower to the Presidency triggers a special election that resets the presidential election cycle. And the major POD here is that Nixon resigns after Agnew but before a new Vice-President is appointed. This can be in late 1973 or early 1974, it doesn't matter -- either way a special election is now scheduled for November 1974. But let's say the latter, for simplicity's sake.
37: Richard Nixon (R) -- 1969-1974 [def. Hubert Humphrey & George McGovern]
The Presidency passes to Speaker Carl Albert. He doesn't want the job, so confirmation of a new Republican Vice-President now goes through the Senate, and Albert resigns. The new President is Gerald Ford, or his TWW equivalent (as in OTL, he was the only Republican the Senate would confirm). These guys are technically Acting Presidents like Glen Allen Walken, so although they count as presidents they don't get numbered.
--: Carl Albert (D) -- 1974
--: Gerald Ford (R) -- 1974-1975
The Democrats unite behind Hubert Humphrey for the special election, who chooses a more conservative running-mate to unite the party (perhaps the TWW equivalent of Scoop Jackson). The Republicans choose presidential & vice-presidential candidates as unrelated to Watergate as possible (say, Ronald Reagan/John Ashbrook). The Democrats still win the election.
38: Hubert Humphrey (D) -- 1975-1978 [def. Ronald Reagan]
Humphrey dies on schedule. [Scoop Jackson*] succeeds him -- as sitting President he is the presumptive nominee, but the public doesn't like him much and an economic downturn doesn't help either. The Republican candidate, a certain Owen Lassiter, wins. (Although Lassiter is the cultural equivalent of Reagan, perhaps he's more identified with John Connally -- as Nixon's successor in a "miss me yet?" kind of way. Like both Reagan and Connally, Lassiter is an ex-Democrat.)
39: [Scoop Jackson*] (D) -- 1978-1979
40: Owen Lassiter (R) -- 1979-1987 [def. [Scoop Jackson*] & [Ted Kennedy*]]
In the 1986 election, the Democrats run D.W. Newman; the Republicans run Lassiter's vice-president. Newman wins. Then in the 1990 election, the Republicans field a centre-right candidate (the equivalent of George Bush) who defeats Newman. The 1994 election is a three-way election, with an independent billionaire-businessman challenger (the equivalent of Ross Perot) -- this guy siphons votes off both parties and ends up getting around 10-15% of the popular vote. [George Bush*] wins reelection with a comfortable electoral-vote victory but the Democratic challenger, a DLP-type Democrat, wins a narrow popular-vote plurality. That's why they take third-party challengers so seriously in the show.
41: D.W. Newman (D) -- 1987-1991 [def. [Lassiter's VP]]
42: [George Bush*] (R) -- 1991-1999 [def. D.W. Newman, [DLP Democrat] & [Ross Perot*]
The 1998 election. The Republican nominee is [George Bush*]'s Vice-President. The Democratic nominee is, of course, Josiah "Jed" Bartlet. [Ross Perot*] also runs again. Bartlet wins with a plurality of the vote; [Ross Perot*] takes about half the votes he got last time. And then Bartlet wins reelection in 2002, as we know, Walken is Acting President for a time, and Santos comes next.
43: Josiah Bartlet (D) -- 1999-2007 [def. [Sitting VP], [Ross Perot*] & Robert Richie].
--: Glen Allen Walken (R) -- 2003
44: Matthew Santos (D) -- 2007-201? [def. Arnold Vinick]
There you have it. It fits all the criteria, and the only thing it doesn't explain is where Bartlet's predecessor was in the episode with Lassiter's funeral. Thoughts?
-- Bartlet was preceded by a two-term centre-right Republican, under whom Leo served as Secretary of Labor
-- Two fictional former Presidents are named: D.W. Newman (one-term Democrat) and Owen Lassiter (two-term Republican).
-- The last real-world President to be named in the show is Richard Nixon
-- There were four Republican presidents between 1969 and 1999 altogether
-- Newman used the same Air Force One as Bartlet
-- Lassiter's former staffers & Cabinet secretaries at his funeral are very old.
The first and last point in particular leads me to believe that Lassiter was not Bartlet's immediate predecessor. Plus the fact that Lassiter is clearly meant as that universe's cultural equivalent of Reagan, and serving 1991-1999 is too late.
So, here's the idea: TWW-universe election law is a little different than ours, in that the ascension of the Speaker of the House or lower to the Presidency triggers a special election that resets the presidential election cycle. And the major POD here is that Nixon resigns after Agnew but before a new Vice-President is appointed. This can be in late 1973 or early 1974, it doesn't matter -- either way a special election is now scheduled for November 1974. But let's say the latter, for simplicity's sake.
37: Richard Nixon (R) -- 1969-1974 [def. Hubert Humphrey & George McGovern]
The Presidency passes to Speaker Carl Albert. He doesn't want the job, so confirmation of a new Republican Vice-President now goes through the Senate, and Albert resigns. The new President is Gerald Ford, or his TWW equivalent (as in OTL, he was the only Republican the Senate would confirm). These guys are technically Acting Presidents like Glen Allen Walken, so although they count as presidents they don't get numbered.
--: Carl Albert (D) -- 1974
--: Gerald Ford (R) -- 1974-1975
The Democrats unite behind Hubert Humphrey for the special election, who chooses a more conservative running-mate to unite the party (perhaps the TWW equivalent of Scoop Jackson). The Republicans choose presidential & vice-presidential candidates as unrelated to Watergate as possible (say, Ronald Reagan/John Ashbrook). The Democrats still win the election.
38: Hubert Humphrey (D) -- 1975-1978 [def. Ronald Reagan]
Humphrey dies on schedule. [Scoop Jackson*] succeeds him -- as sitting President he is the presumptive nominee, but the public doesn't like him much and an economic downturn doesn't help either. The Republican candidate, a certain Owen Lassiter, wins. (Although Lassiter is the cultural equivalent of Reagan, perhaps he's more identified with John Connally -- as Nixon's successor in a "miss me yet?" kind of way. Like both Reagan and Connally, Lassiter is an ex-Democrat.)
39: [Scoop Jackson*] (D) -- 1978-1979
40: Owen Lassiter (R) -- 1979-1987 [def. [Scoop Jackson*] & [Ted Kennedy*]]
In the 1986 election, the Democrats run D.W. Newman; the Republicans run Lassiter's vice-president. Newman wins. Then in the 1990 election, the Republicans field a centre-right candidate (the equivalent of George Bush) who defeats Newman. The 1994 election is a three-way election, with an independent billionaire-businessman challenger (the equivalent of Ross Perot) -- this guy siphons votes off both parties and ends up getting around 10-15% of the popular vote. [George Bush*] wins reelection with a comfortable electoral-vote victory but the Democratic challenger, a DLP-type Democrat, wins a narrow popular-vote plurality. That's why they take third-party challengers so seriously in the show.
41: D.W. Newman (D) -- 1987-1991 [def. [Lassiter's VP]]
42: [George Bush*] (R) -- 1991-1999 [def. D.W. Newman, [DLP Democrat] & [Ross Perot*]
The 1998 election. The Republican nominee is [George Bush*]'s Vice-President. The Democratic nominee is, of course, Josiah "Jed" Bartlet. [Ross Perot*] also runs again. Bartlet wins with a plurality of the vote; [Ross Perot*] takes about half the votes he got last time. And then Bartlet wins reelection in 2002, as we know, Walken is Acting President for a time, and Santos comes next.
43: Josiah Bartlet (D) -- 1999-2007 [def. [Sitting VP], [Ross Perot*] & Robert Richie].
--: Glen Allen Walken (R) -- 2003
44: Matthew Santos (D) -- 2007-201? [def. Arnold Vinick]
There you have it. It fits all the criteria, and the only thing it doesn't explain is where Bartlet's predecessor was in the episode with Lassiter's funeral. Thoughts?