The Republican Party was formed in 1854. It was a fusion of many different parties, some of which completely dissolved in order to form this new party. The reason they were willing to take such a drastic step is that there was one issue about which they felt so strongly, that this became the overriding factor - slavery.
Whigs were the prominent second party in the 1830's-1850's, but were a minority, weilding not enough power to get things done over the Democrats. Other smallers groups that were anti-slavery - Free-Soilers, Know-Nothings, Free Democrats, and others - were also far too small to make a difference.
When the Kansas-Nebraska Acts were passed and the Missouri Compromise repealed, this was taken as a betrayal of trust and faith by the Northern anti-slavery groups. The Missousi Compromise, in particular, was almost revered. Unable to fight the spread of slavery on their own, these various groups combined to form the Republican Party in 1854.
The Platform of the Republican Party started with and announced as its primary goal, the elimination of slavery at the soonest possible moment, and the stop of the spread of it to new state immediately. There were economic and other goals, too, but this was the reason the party was formed and its #1 stated quest.
The Republican Party wasn't even called that by many of these fusion candidates in 1854 and 1855, but by 1856 the Republican Party was by name represented in most states. It continually gained strength throughout the 1850's, both locally, statewide, and nationhally, finally electing a majority in congress and well as a President in 1860.
The goals of the Republican Party outside of Slavery involved increased tariffs to protect home-based industries, hard money policies, and more - but unqiestionably the party was formed for, and dedicated to, the elimiation of slavery - that goal brought the adversaries together.
Below is one of the annoucements of a meeting (1854) called to form this new party. This was from Michigan, and was one of many such announcement and meetings. It's a fascinating story:
"TO THE PEOPLE OF MICHIGAN"
A great wrong has been perpetrated. The slave power of this country has triumphed. Liberty is trampled underfoot. The Missouri compromise, a solemn compact, entered into by our fathers, has been violated, and a vast territory dedicated to freedom has been opened to slavery.
This act, so unjust to the North, has been perpetrated under circumstances which deepen its perfidy [treachery]. An administration placed in power by Northern votes has brought to bear all the resources of executive corruption in its support.
Northern Senators and representatives, in the face of overwhelming public sentiment of the North, expressed in the proceedings of public meeting and solemn remonstrances [protest], without a single petition in its favor on their table, and not daring to submit this great question to the people, have yielded to the seductions of executive patronage, and, Judas-like, betrayed the cause of liberty; while the South, inspired by a dominant and grasping ambition, has, without distinction of party, and with a unanimity almost entire, deliberately trampled under foot the solemn compact entered into in the midst of a crisis threatening the peace of the Union, sanctioned by the greatest names of our history, and the binding forces of which has, for a period of more than thirty years, been recognized and declared by numerous acts of legislation. Such an outrage upon liberty, such a violation of plighted faith, cannot be submitted to. The great wrong must be righted, or there is no longer a North in the councils of the nation. The extension of slavery, under the folds of the American flag, is a stigma upon liberty. The indefinite increase of slave representation in Congress is destructive to that equality between freemen which is essential to the permanency of the Union.
The safety of the Union -- the rights of the North -- the interests of free labor -- the destiny of a vast territory and its untold millions for all coming time -- and finally, the high aspirations of humanity for universal freedom, all are involved in the issue forced upon the country by the slave power and its plastic Northern tools.
In view, therefore, of the recent action of Congress upon this subject, and the evident designs of the slave power to attempt still further aggressions upon freedom -- we invite all our fellow citizens, without reference to former political associations, who think that the time has arrived for a union at the North to protect liberty from being overthrown and downtrodden, to assemble in mass convention on Thursday, the 6th of July, next, at 4 o’clock, P.M., at Jackson, there to take such measures as shall be thought best to concentrate the popular sentiment of this State against the aggression of the slave power."
This meeting was attended by people from all parties, and they formed an election ticket of Free Democrats, Free Soilers, Whigs, and more - now all calling themselves Republican.
Zachariah Chandler, a devout Whig, said:
"Misfortunes make strange bedfellows. I see before me Whigs, Democrats and Free-Soilers, all mingling together to rebuke a great national wrong. I was born a Whig; I have always lived a Whig and hope to die fighting for some of the Whig doctrines. But I do not stand here as a Whig. I have laid aside party to rebuke treachery."
The Republican Party was founded on, and throughout the 1850's primarily existed to, stop slavery.