Here is my attempt at a semi-unrealistic timeline.
After three years of Bill Clinton in office, Colin Powell had generally refused to run for the President of the United States. His successes as the Chairman of the Joint Chiefs of Staff, and the National Security Advisor in the Reagan administration had made him a favorite for the Republicans, particularly among the moderates who feared the selection of a radical Republican during the primaries in 1996. Dole was a major front-runner, but Powell was still ahead in general for polls for the primaries. Powell in July 1995 announced his intention to run for the President of the United States after nearly being drafted by base Republicans. Dole, Powell, and Pete Wilson (Who never got throat surgery, allowing his campaign to take off). Dole surged in the early primaries, but after Wilson dropped out and endorsed Powell, and the endorsement from John McCain, Rudy Giuliani, and many other moderate Republicans, Powell won the Republican primaries and the nomination. He selected John McCain to be his running mate.
Powell/McCain quickly became a popular ticket for moderates on both sides of the political spectrum. For older Republicans, Powell reminded them of Eisenhower, while younger Republicans thought of Powell as a modern Nelson Rockefeller. They ran on a fiscally conservative and socially liberal (Or socially centrist) platform during the campaign against Clinton. Powell particularly attacked Clinton, calling him a "Draft Dodger". Powell's support from moderates won him many states in New England, his native New York, and New Jersey, but his socially liberal/centrist views lost him votes to Ross Perot in the south (Leading to some states going to Clinton/Gore). Powell won the Presidential election by just a small margin.
Colin Powell (R-NY) and John S. McCain (R-AZ): 277 EV (50%)
William J. Clinton (D-AK) and Al Gore (D-TN): 261 EV (47%)
Powell took office as President of the United States on January 20th, 1996, becoming the first African-American President. Powell selected a bipartisan Cabinet, selecting several Democrats for major key positions in his administration, saying that "Party opinions end on the lawn", wishing for an administration with a wide variety of opinions. The highest ranking Democrat in the Powell Administration was Secretary of State John Kerry, a Democrat from Massachusetts. It was rumored that Al Gore was offered the position initially, but he refused. The Powell Administration quickly took action against NAFTA, as well as taking action in Yugoslavia throughout 1999 and 2000 to take action against the ethnic cleansing in the area. Powell also sought to reform the United States military by training for small-scale operations rather than large-scale operations (Which would come in use later on). During Powell's first term, his Administration had immense public support, and support from both Democrats and Republicans in the Congress. By the 2000 election season, the economy was improving greatly, and things seemed good for Powell/McCain. The Democrats had nominated Paul Wellstone to run against Powell/McCain. Wellstone chose Dick Gephardt as his running mate for the 2000 election.
The 2000 election was a massive electoral landslide for Powell, as well as one of the largest popular vote landslides in American history. Powell's moderate campaign had stolen the moderate vote from the Democrats, but this left the conservatives in the south somewhat angered by Powell's moderate views on abortion and gun control. He lost Mississippi and Arkansas as a result, but won the election otherwise.
Colin Powell (R-NY) and John S. McCain (R-AZ): 501 EV (60%)
Paul Wellstone (D-MN) and Dick Gephardt (D-MO): 37 EV (38%)
The second term of the Powell Administration saw many changes for the world. Less than a year into his second term, the United States was attacked by terrorists from Al-Qaeda. 3500 Americans were killed when planes crashed into the World Trade Center, Pentagon, and the United States Capitol Building. 2 Senators and 8 Representatives who were near the crash site during an evacuation of major officials in the city were killed. Powell's approval rating skyrocketed following the attacks, leading the United States into the first major war of the 21st century. The United States invaded Afghanistan in December 2001, overthrowing the Taliban and using small-unit operations to wipe out Taliban resistance. A major occupation force was set up from 2001-2005, and a pullout of most US troops occurred by 2005. Another issue was that of Syria, which had supported a terrorist group that attacked London and Boston in 2003. While Iraq also supported the group, Powell wanted to contain Iraq, while intervening in Syria. In late 2003, the United States, NATO, and several other countries invaded Syria, once again setting up a provisional government, and pulling out within four years time. In 2004, two weeks before the Presidential election, Osama Bin Laden was killed along the Pakistani border by United States special forces.
The 2004 Presidential election was a quick one for the Republicans, or at least selecting their candidate. Rudy Giuliani, the Mayor of New York City during 9/11, and the Governor of New York State since 2003, was quickly selected as the nominee, selecting Tom Tancredo as his Vice Presidential nominee. The Democrats selected Gary Hart as their Presidential nominee. He chose John Edwards as his Vice Presidential nominee. Rudy Giuliani, largely being carried by support from Colin Powell's Presidency, won the 2004 Presidential election.
Rudy Giuliani (R-NY) and Tom Tancredo (R-Colo.): 482 EV (55%)
Gary Hart (D-Colo.) and John Edwards (D-NC): 56 EV (44%)
Rudy Giuliani, like Powell, selected a bipartisan cabinet, choosing Joe Lieberman as his Secretary of State. Giuliani continued with the same initial popularity that Powell had. The War in Afghanistan was coming to a complete end by early 2006, and the War in Syria was finishing up as well. Osama Bin Laden was dead, but Saddam Hussein was becoming a greater thorn in the side of the United States. Rudy Giuliani would continue on with a second term, winning in 2008 with a much smaller margin than he did in 2004. The Republican party had largely become a more moderate party, leading to the Democrats by 2007 starting to move to the center, with the Democrats regaining support in the south, while the Republicans started to once again dominate the north and the west coast.