With the exceptions of Ronald Reagan in 1984 and FDR in 1936. FDR and Reagan were both transformative Presidents who changed the political landscape by passing programs that linked many voters to them and their parties for years to come. They are the exceptions here.
Here are the unemployment rates at reelection time for every President reelected since 1948.
2004, Bush(R): 5.4%
1996, Clinton(D): 5.4%
1984, Reagan(R): 7.2%
1972, Nixon(R): 5.3%
1964, Johnson(D): 4.8%
1956, Eisenhowr(R): 4.3%
1948, Truman(D): 3.8%
Average: 5.2%
Unless Obama can pass healthcare reform, which would link many new voters to him and the Democratic party as Social Security and public works programs did for FDR and tax cuts did for Reagan, he will not be reelected unless unemployment falls below 6% in the next two years.
I agree passing healthcare reform is important, but suggesting if healthcare isn't passed he is doomed if unemployment isn't below 6% is a little far fetched. One caveat you leave out is the unemployment rate when those Presidents all took office.
The BLS site doesn't show where it was in 45 when Truman took over following FDR's death, but in the cases of Ike, Johnson, Nixon and Bush the unemployment rate was under 6% for all of them when they took over. In fact for Ike, Nixon and Bush it was below 4%. Unemployment for Reagan was pretty much where it was when he took over, went up during his first two years, declined the next to, ending up basically where it started off. So out of all of those you listed that were reelected with unemployment under 6%, Clinton was the only one who took over with unemployment above that figure.