Final answer:
The statement is False. Lincoln did believe the national government had the power to end slavery in certain areas and aimed to do so with the Emancipation Proclamation.
Step-by-step explanation:
The statement 'Although Lincoln was opposed to slavery, he did not think that the national government had the power to end it in slave states' is False.
Abraham Lincoln, while initially aiming to preserve the Union, eventually issued the Emancipation Proclamation in 1863 to free enslaved people in the rebellious states. This demonstrates that Lincoln did believe the national government had the power to end slavery in certain areas.
Additionally, Lincoln's quote about the government becoming 'all one thing, or all the other' suggests his belief that slavery needed to be ended nationwide.