Question

What is Calhoun's main claim in the speech?

"There is and always has been in an advanced stage

of wealth and civilization, a conflict between labor and
capital."
"All we want is concert, to lay aside all party

differences and unite with zeal and energy in repelling
approaching dangers."
"... the relation now existing in the slaveholding

States between the two, is, instead of an evil, a good
-a positive good...."
"... in few countries so much is left to the share of the
laborer, and so little exacted from him

Answer 1

It is not specified which speech by Calhoun is being referred to in the question, but I can provide the main claims from several of his notable speeches:

[I] In the speech "Slavery a Positive Good" delivered in 1837, Calhoun argues that slavery is a beneficial institution for both the slave and the slaveholder, and that attempts to abolish it would lead to disastrous consequences.

[II] In the speech "A Disquisition on Government" delivered in 1849, Calhoun claims that the best way to prevent tyranny is to divide power among different levels of government and to create a system of checks and balances.

[III] In the speech "The Concurrent Majority" delivered in 1850, Calhoun argues that the only way to prevent conflict between different sections of the country is to give each section a veto power over federal legislation that affects their interests.

Without more information on which specific speech is being referred to, it is difficult to provide a more precise answer to the question...