The way in which G.H.W. Bush would have been reelected would have been for the economic uptick that started in October 1992 to start a month or two earlier. Bush-Qualye 1992 was able to significantly close the gap between Clinton-Gore by focusing on economic growth and throwing around that scary word "liberal" when describing his Southern centrist opponents. Had the economy shown growth signs and the October 1992 Iran-Contra revelations against Bush not been released Bush could well have won a narrow reelection:
Bush/Quayle (R): 282 EVClinton/Gore (D): 256 EVPerot/Stockdale (I): 0 EV The states of Pennsylvania, Maine, New Hampshire, New Jersey, Nevada and Ohio are all decided by less than 10,000 or so votes. Thus, the 1992 election probably would have had numerous state election recounts, but for sake of the thread President Bush survives these issues.
The second term of George Herbert Walker Bush leaves many questions in terms of fiscal and foreign policy. In terms of fiscal policy Bush could either follow the path of the first term (raising taxes to battle rising deficits) or govern as his son did with expansionary fiscal policies (cutting taxes on the wealthy while increasing spending). Let's say that Bush, having been reelected in an upset, is feeling that he has much political capital to spend (as his son bragged in 2004 despite being reelected by 3% of the vote) and goes for broke in the fiscal realm. He fights for the 1993 Bush Tax Cuts which are attacked by Speaker Tom Foley as being "plain and simple tax cuts for the rich" and lamented by conservative fiscal hawks as "unnecessary economic stimulus which will only increase the national debt." Despite these attacks, the appeal of a tax cut proves too much for the Congress and an amended across the board tax cut is approved, but the wealthy benefit the most.
There will be no Hillary-care debacle, but President Bush pushes Medicaid and Social Security reform acts which focus on "private sector solutions." The Grey Panthers, AARP and other senior citizens groups attack this idea and debate over the plan is the marquee issue of the 1994 midterm elections.
The H.W. Bush second term foreign policy is not an easy one to pinpoint. Brent Scowcroft was not a neoconservative and wisely opposed deposing Hussein in 1991. Secretary of Defense Dick Cheney also shared this opinion, amazing enough. I do not think that neoconservatives would be happy with a second term of H.W. Bush simply because he was not a student of Strauss or Kroeger and let very few neoconservative thinkers into his state or defense departments. I think that his second term foreign policy would reflect the first Clinton Administration's foreign adventures. Thus the intervention if Somalia, which Bush had approved of in his first term, would still occur and favorable trade relations with China and Vietnam would be approved of by the administration. In Rwanda Bush, like Clinton, would have left it up to the UN to handle the genocide. In the Balkans Bush may have begun bombings in 1993 or 1994 and would have ended the arms embargo on the former Yugoslavia, hurting American relations with Western Europe and cementing leftist movements in Central and Western Europe into the popular conscience of voters. Thus, you could see Chirac lose reelection as Mayor of Paris and never rise to the presidency of France and an earlier collapse of the Major government in the UK.
The 1994 midterm elections would have been a wash because the expanding economy would have helped Republicans but the "six year curse" would have benefited the dominant Democrats, thus the Democrats remain in control of Congress and there is no Speaker Newt Gingrich and probably no Senator Rick Santorum (of which I would not miss either).
The Bush Administration may well have seen scandals arise. I doubt Bush would have pardoned Casper Weinberger and the five other Iran-Contra figures thus leading to a trial where the truth about that sorry episode may well have come out, embarrassing the administration. After the 1993 WTC bombing and the 1995 Oklahoma City bombing Republicans may have called on their Republican president to "get tough on terror." While I do not see a huge new federal agency being established, Attorney General Giuliani (after losing the 1993 NYC mayor race he is given a consolation prize by Bush) overseeing a large crack-down on militia groups and investigations into terror groups.
In 1996 the country would have no doubt been sick of Republicans in the White House. The establishment of the Democratic Party selected Senator Jay Rockefeller of West Virginia as their nominee after a short primary battle with Senators Al Gore and John Kerry. The Republicans see a right-wing insurgency against Vice-President Quayle which knocks the veep out of the 1996 primaries fairly early. Former Secretary of Defense Dick Cheney and Senator Phil Gramm of Texas battle one another for most of the race with Cheney emerging as victor but insurgent conservatives dominating the platform committee and the convention. The 1996 election is an easy win for Rockefeller:
Rockefeller/Ben Nelson (D): 335 EVCheney/Gingrich (R): 203Perot/Choate (Ref): 0 EV 
