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Here's a thing.

[Taken from web.themaproom.fan/spec/presidents, retrieved February 2015. Links removed.]

1600 Penn - A List of Presidents

Real:
...
1963-1969: Lyndon B. Johnson/Hubert H. Humphrey (D) [see Netpedia]

In-Show:
1969-1977: William Stanford (R) [1]
1977-1981: Douglas McFarland (D) [2]
1981-1989?: Jim Briggs (R) [3]
1989-1993: Orrin Michaels (D) [4]
1993-2001: Kay Wood (R) [5]
2001-2007: Michael Baker (D) [6]
2007-2009: Janine Ford (D) [7]
2009-present: Thaddeus Rice (R) [8]

[1]: Mentioned in several episodes, notably 1009 Sub Rosa. Defeated Tom Paxton, father of Kevin Paxton, in 1972 election. During 1009 Sub Rosa, revealed that Stanford used illegal means to win 1972 election, including bugging Paxton's office. Oversaw Aeneid program, Hartford Accords, creation of ERC. Former New York Senator. Played in archival footage by Greg Williams. Based on President Richard Nixon, with elements of Nelson Rockefeller.
[2] Appears in 0204 Trade Deficits and mentioned in several others, notably 0612 On The Shoulders Of Giants. Moderate Democrat, opposed Baker from the right, especially on economics. Vice President was John Price. Attorney General was Tom Paxton. Secretary of Transportation was Hobart Edwards. Died during Season 6. Former Senator. Southerner. Played by Ivan Norris. Based on President Lloyd Bentsen.
[3] Mentioned in several episodes. Republican, considered conservative. Appointed Chief Justice Todd Mathers to the Supreme Court. Secretary of State was Harris Lee. Secretary of Commerce was presumably Richard Reinhardt. Based on President John Connally, but unlike him, seems to have served full terms.
[4] Appears in several episodes, notably 0804 The War On War. Democrat, moderate. One-term President, appointed UN Ambassador by President Baker. Counseled Baker to accept the failure of the Athens talks and move on. As President, known for arms reduction treaties and poor response to economic downturn. See Cabinet. Played by Martin Garrison. Loosely based on President Gary Hart.
[5] Appears in several episodes, notably 0305 Exhibit H and 0910 Spokane, America. First female President. Criticized Baker for scandals and "ignoring ordinary America". As President, known for economic boom and late-term crash, as well as hawkish foreign policy. See Cabinet. Played by Deborah Thompson. Based on President Richard Lugar, with elements of Vice President Lynn Martin.
[6] See Michael Baker. Former Governor of Virginia. First African-American President. Resigned in second term due to health reasons. Played by Aaron Jackson. Loosely based on President Henry Cisneros.
[7] See Janine Ford. Former Wisconsin Senator. Appointed Vice President at 2004 DNC after retirement of Matt Kelley, ascends to Presidency after Baker's resignation. Based on then-Attorney General Elizabeth Warren, with elements of President Tim Kaine.
[8] See Thaddeus Rice. Former Montana Governor. Elected President in 2008 election. Moderate Republican. President as of Season 14, likely to be the final season. Based on Governor and later President John Thune.