Does "won without carrying a single Southern state" mean...?

Does "won without carrying a single Southern state" mean "won without winning over a single Southern state"?
And " losing representation" mean "losing seats in Congress (or seats of app:ds:the House of Representative and the Senate)"?
Context:

Causes of secession

Main articles: http://en.wikipedia.org/wiki/Origins_of_the_American_Civil_War, http://en.wikipedia.org/wiki/Timeline_of_events_leading_to_the_American_Civil_War, and http://en.wikipedia.org/wiki/History_of_the_United_States

The causes of the Civil War were complex and have been controversial since the war began. The issue has been further complicated by http://en.wikipedia.org/wiki/Historical_revisionism, who have tried to offer a variety of reasons for the war.^[9] Slavery was the central source of escalating political tension in the 1850s. The http://en.wikipedia.org/wiki/RepublicanParty(United_States) was determined to prevent any spread of slavery, and many Southern leaders had threatened secession if the Republican candidate, http://en.wikipedia.org/wiki/Abraham_Lincoln, won the http://en.wikipedia.org/wiki/1860_U.S._Presidential_election. After Lincoln had won without carrying a single Southern state, many Southern whites felt that disunion had become their only option, because they felt as if they were losing representation, which hampered their ability to promote pro-slavery acts and policies.^[10]