Abraham Lincoln, perhaps our greatest President, gets the honor for being the most unpopular, and got assassinated to boot.
Known almost exclusively by his got-up nickname "The Railsplitter," Lincoln had won the 1860 election in November with 39.8 percent of the popular vote. This absurdly low total was partly due to the fact that four candidates were on the ballot, but it remains the poorest showing by any winning presidential candidate in American history
At the time he was sworn in, Lincoln's "approval rating" can be estimated by examining wintertime Republican losses in local elections in Brooklyn, Cincinnati, Cleveland and St. Louis, and state elections in Connecticut, Massachusetts and Rhode Island; by the observations of Henry Adams (of the presidential Adamses) that "not a third of the House" supported him; and by the published reckoning of the New York Herald that only 1 million of the 4.7 million who voted in November were still with him. All these indications put his support in the nation at about 25 percent — roughly equivalent to the lowest approval ratings recorded by modern-day polling.
The linked article goes to great lengths to demonstrate the vitriol the first Republican president faced in office. It's worth a read in its entirety. It's also worth noting that seven states seceded from the Union after his election but before his swearing in.
For modern era Presidents you can go here. Truman heads the list. http://us-presidents.insidegov.com/stories/5342/least-most-popular-presidents#24-Eisenhower-Overview