There were fifteen slave states. If all had opposed the amendment it would have taken 46 states to ratify it. Do the math.
Doing the math, as you suggest, reveals that President Lincoln simply did not have the votes necessary to abolish slavery peacefully through the U.S. constitution's amendment process.
If Lincoln wanted to abolish slavery, he would have to do it through force of arms - in other words, use violence to overthrow the pro-slavery U.S. constitution and to kill or imprison anyone who opposed.
For that he would need a pretext for war which he found in the Gulf of Tonkin incident. I meant to say the Fort Sumter incident.