I'm going to assume you mean a PoD of 1945 or later, because if not, that's oddly specific.
Here it is: Nixon decides to adequately prepare for the first debate with Kennedy. Nixon gains momentum and narrowly wins the Election of 1960. He becomes President, and Henry Cabot Lodge becomes Vice President. Nixon in TTL governs as a moderate; in fact, his policies become very similar to Kennedy's in OTL. On November 22, 1963, a crazed Lee Harvey Oswald assassinates President Nixon; Lodge, a notorious moderate, becomes the President. After winning the Election of 1964 with his running mate Nelson Rockefeller against Hubert Humphrey, pursues a new agenda. He moves to the left of Nixon, pursuing Civil Rights a la Johnson (but without the Great Society). This angers the right wing of the Republican Party, but attracts the left wing of the Democratic Party to the Republicans. In 1968, the fractured Democrats nominate George Wallace, while the Republicans nominate William Scranton. Predictably, Scranton wins.
The left wing begins to emigrate en masse to the Republicans in light of this string of four moderate Republican Presidents. Additionally, Henry "Scoop" Jackson takes a harder right than he does in OTL, becoming the darling of the right wing. Several high-profile conservatives, including Barry Goldwater, become Democrats. As a counter to this move, most of the left wing of the Democratic Party joins the Republicans. Scranton decided that he would not run for reelection in 1972, opening the nomination up to the field. The Republicans nominate former Democrat Eugene McCarthy, while the Democrats nominate Scoop Jackson. Jackson wins the Presidency, and his running mate, former Republican Barry Goldwater, becomes Vice President. This solidifies the GOP as the left-wing party and the Democrats as the right-wing party.
After Jackson serves two terms, Goldwater, feeling he is too old to serve, chooses not to run. The Democratic Party enters a bitter race between Senator Bob Dole and Texas Governor George (HW) Bush. Bush managed to eke out a win. He chooses Dole as his running mate. The Republicans nominate Jerry Brown, who chooses Hubert Humphrey as his running mate. Capitalizing on Jackson's populartity, George Bush becomes the President of the United States, giving the Democrats four more years in the White House.