This is a possibly unintentional misstatement of what Lincoln said in his speech.
At the time Lincoln and a great many other Free Soil men believed there was a conspiracy among southerners, using the power of the federal government, to force slavery on the rest of the states. There was some evidence at the time and since to support this position. That is what he was concerned about.
Lincoln himself at the time of this speech and up to the Emancipation Proclamation recognized the federal government as having no power to interfere with slavery within a state. He even recognized this in the EP, as it affected only areas in rebellion against the Union.
Not so. The south seceded from the Union. They just wanted to be left alone. Why would they try to force slavery on all the states when slavery was legal, alive and well in the northern states already? Lincoln wanted no part of the slavery issue at the time. He just wanted to keep the Union together. He even stated words to that effect.