By John Dodge

CHICAGO (CBS) — It would be a good narrative, if it were only true.

At an event promoting her new book “Hard Choices,” Hillary Clinton spoke on Wednesday about how she and Mayor Rahm Emanuel were good friends and that she admired his political rise. She joked that she wrote about him in the first chapter of the book but asked him not to read it–an apparent good-natured jibe at the mayor’s notorious temper. (The portion in the chapter is quite positive.)

Early in the 2008 primary, Emanuel stayed neutral but eventually backed Barack Obama and served as his first chief of staff. Clinton, of course, became Obama’s secretary of state.

At Wednesday’s Emanuel-Clinton symposium for her book tour, Clinton said: “I actually write about Rahm in the book. I asked him not to read it before we sat and did our interview! But it was in the very first chapter, the chapter I rightly call ‘Team of Rivals’ because that’s what it was in the beginning. A senator from Illinois ran against a senator from New York just as had happened way back with a senator from Illinois named Lincoln and a senator from New York named Seward. And it turned out the same way.”

The problem: Lincoln was never a U.S. senator. In fact, he lost twice–in 1855 to Lyman Trumbull (the state legislature selected Trumbull over Lincoln) and then lost in an election to Stephan Douglas three years later.

Lincoln won the 1860 Republican presidential nomination over William Seward, the U.S. senator from New York who had been considered a favorite.

Seward later became Lincoln’s Secretary of State–that is at least a parallel between Clinton and Obama, and she writes about that in the book as she considers Obama’s offer to hold the same Cabinet position.

She writes that Emanuel, as chief of staff, would “provide the initial glue” that would hold the former primary rivals together. She also writes about the parallel with her career and Seward’s but doesn’t refer to Lincoln as a senator in the book.

Opponents seized on Clinton’s historical gaffe just like they did when she said she and President Bill Clinton were “dead broke” after they left the White House.

Here is Mr. Lincoln’s biography on the Biographical Directory of the United States Congress

LINCOLN, Abraham, a Representative from Illinois and 16th President of the United States; born in Hardin County, Ky., February 12, 1809; moved with his parents to a tract on Little Pigeon Creek, Ind., in 1816; attended a log-cabin school at short intervals and was self-instructed in elementary branches; moved with his father to Macon County, Ill., in 1830 and later to Coles County, Ill.; read the principles of law and works on surveying; during the Black Hawk War he volunteered in a company of Sangamon County Rifles organized April 21, 1832; was elected its captain and served until May 27, when the company was mustered out of service; reenlisted as a private and served until mustered out June 16, 1832; returned to New Salem, Ill., and was unsuccessful as a candidate for the State house of representatives; entered business as a general merchant in New Salem; postmaster of New Salem 1833-1836; deputy county surveyor 1834-1836; elected a member of the State house of representatives in 1834, 1836, 1838, and 1840; declined to be a candidate for renomination; admitted to the bar in 1836; moved to Springfield, Ill., in 1837 and engaged in the practice of law; elected as a Whig to the Thirtieth Congress (March 4, 1847-March 3, 1849); did not seek a renomination in 1848; an unsuccessful applicant for Commissioner of the General Land Office under President Taylor; tendered the Governorship of Oregon Territory, but declined; unsuccessful Whig candidate for election to the United States Senate before the legislature of 1855; unsuccessful Republican candidate for the United States Senate in 1858; elected as a Republican President of the United States in 1860; reelected in 1864 and served from March 4, 1861, until his death; shot by an assassin in Washington, D.C., April 14, 1865, and died the following day; lay in state in the Rotunda of the U.S. Capitol, April 19-21, 1865; interment in Oak Ridge Cemetery, Springfield, Ill.

Watch & Listen LIVE