You are in error. Buchanan had his own set of competing proposals that he was trying to pitch. He recruited Gen. Duff Green to try and get Lincoln on board with him, but Lincoln refused.
Lincoln refused because he had his own plot in the works - the Corwin amendment. The Corwin amendment was first proposed by William Seward, NOT Buchanan. Seward introduced its full text in the Committee of Thirteen just before Christmas in 1860. Seward did this after meeting with Thurlow Weed, who had come straight from Springfield carrying a message from Lincoln to introduce it.
When Lincoln arrived in Washington in February the measure was on the verge of coming up for a vote - so he went to work immediately lobbying for the thing as reported openly in the newspapers and recorded to history by Henry Adams, whose father - another loyal Lincolnite - was one of the House sponsors. Lincoln even slipped into the senate gallery while they were debating it to catch a glimpse of the events. Thus, when he claimed the next day that he had not seen the amendment yet, he was lying. He had not only seen it - he helped write the thing!
"Each house of Congress established a committee to deal with the crisis. The House moved first, setting up on 4 December - the day of Buchanan's message - a committee containing one member for each of the thirty-three states. Two weeks later the Senate joined the compromise efforts. The Senate's Committee of Thirteen included the most important national figures in the Senate: Stephen Douglas, Jefferson Davis, John J. Crittenden, and William Seward. Although the two committees seemed to operate independently their efforts were linked by a desire to find proposals that would appeal to as much of the disaffected South as possible. Northern Democrats and border slave-state legislators were most active with plans, but interestingly enough,the most well-known Republican had a major role in the process.
"William Seward served only on the Senate committee, but he worked intently on shaping policy in both houses. He was a constant visitor at the Washington home of Charles Francis Adams, perhaps the most important member of the Committee of Thirty-three. Seward encouraged proposals that emerged from both committees in the attempt to reassure the South while maintaining Republican support.
"From the Senate committee came proposals under Crittenden's names: slavery within the states to be protected from national government interference; the revival of the Missouri Compromise line - no slavery above 36 degrees 30 minutes north latitude, slavery permitted below that line in territories held or to be acquired later; no cessation of slavery in the District of Columbia unless Maryland and Virginia agreed; no interference by Congress with interstate slave trade; slaveholders who lost runaways to the northern states to be compensated. Slavery was thus to be protected from every imaginable use of national authority and would be secure in existing southern states. Most important, if the United States expanded into Central America and the Caribbean, slavery would expand too. For some time Seward let people believe that he might favor this "Crittenden Compromise."
"From the Committee of Thirty-three came more moderate proposals with a two-fold purpose. First, to settle the crisis the South was promised that the fugitive slave law would be enforced and that state personal liberty laws, which conflicted with slave catching, would be repealed. In addition came a nonamemdable constitutional amendment [the "Corwin Amendment"] protecting slavery in the states from any form of federal interference. The second purpose was to divide the South if it could not be placated, to detach the already seceded lower south from the upper south, where secession was still being debated. The divisive proposal rested on the admission of New Mexico to the Union as a state. No mention was made of slavery, but the territory had a small number of slaves and a slave code to protect them. Because the climate and soil forecast a bleak future for slavery, however, many observers believed that slavery would soon die there. The lower south legislators opposed the New Mexico measure, but the upper south lawmakers supported it. Lincoln allowed the New Mexico idea to flicker.
"Lincoln accepted most of these measure with one crucial exception.... [t]he key Republican bedrock - no expansion of slavery into the territories. When word leaked out that such a proposal might be offered, Lincoln acted quickly and forcefully. He wrote Lyman Trumbull on December 10, William Kellogg the next day, Elihu Washburne two days later, Trumble again, and Thurlow Weed on the 17th, and John Defrees the next day, with one thundering message: "'Let there be no compromise on the question of extending slavery.'"
From The Presidency of Abraham Lincoln by Phillip Shaw Paludan, pp 31-32
Several things here refute your story.
(1) The "Corwin Amendment" was introduced in the House Committee of Thirty-three. Seward was not a member of the House.
(2) Seward was on the Senate Committee of Thirteen, but that committee did not propose an amendment.
(3) Lincoln remained in Illinois and corresponded by letter - an extremely slow method to conduct secret plots at distance.
(4) Lincoln was making few, if any, public statements at the time.
(5) Lincoln was corresponding with Thurlow Weed, in Washington, by mail.