If President Obama were running for re-election today, could he win?
In a literal sense, "...it depends on the opponent" is the correct answer, as all things are relative. But, this question is intended to explore the man's stature in the political world in general, and how it has fallen and/or survived.
Let’s rephrase the question, could a president win re-election with a 40% approval rating which the president is at today? Obama won re-election with a 52% approval rating back in 2012. There is more to it than just approval ratings as I think one must also take into consideration party affiliation/identification strength. That information I have, but it would take time to compile both approval and party affiliation. So let’s just look at the approval rating
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Bush the second was at 53% approval when he won re-election in November of 2004, Bush won a fairly close race 51-48%. Obama’s re-election he won 51-47 with almost the identical approval rating.
Clinton was at 58% in 1996, he won easily over Bob Dole
Bush the first 1992 was at 34% and he lost decisively
Reagan 1984 was at 61% and it was no contest
Carter 1980 was at 37% and he got whopped.
Ford is more an asterisk in that he was completing Nixon’s second term, but he was at 45% when he narrowly lost to Jimmy Carter.
Nixon in 1972 was at 62% when he gave McGovern a drubbing
JFK was assassinated and LBJ decided not to run.
Eisenhower was at 68% and another easy winner
This is where presidential approval ratings end that are of any use. I think we can safely assume the closer to the 50% mark in the approval ratings the closer the election is for the winner. But every president with an approval rating of 50% or higher above won his re-election bid. We can safely assume that any president below 40% is a loser as seen in Carter and Bush the first. Ford barely lost, he was below 50% at 45%. Can we safely assume that any president at 45% approval rating or lower would lose, no. One example is just that, an example. But I do think a president running for re-election at least has to be in the upper 40’s. Perhaps 48% is the cut off, but that is just an educated guess, SWAG.
To be certain I would have to go back and add the political party affiliation to the equation. But just based on the above if President Obama was running for re-election today, he would lose.