Here is historian Michael Medved’s description of that history. By the way, the Whigs were only a party for 22 years.
“2. NO, THE REPUBLICANS NEVER CONSTITUED A THIRD PARTY
Whenever I take the time on the radio to discuss the obvious and inevitable futility of minor party campaigns, some smug caller will try to play “gotcha” by reminding me that my own beloved GOP began its political life as a minor party, and managed to elect an underdog nominee named Lincoln in the fateful election pf 1860. It makes for a good story, and I know it allows misled minions to feel better to believe that it’s true, but the Republicans never operated as a third party. By the time of the first Republican County Convention (in Ripon, Wisconsin, on March 20, 1854) the Whig Party had already collapsed and shattered, hopelessly divided between its Northern anti-slavery branch and the Southern “Cotton Whigs.” Refugees (including numerous Congresmen, Senators and others) from the Whig debacle determined to fill the vacuum and, joined by a few anti-slavery Democrats and former Free Soilers, they launched their new national organization.
The first time candidates ever appeared on ballots with the designation of the new Republican Party came with the Congressional elections of 1854 and the fresh organization won stunning success from the very beginning. That very first year the Republicans won the largest share of the House of Representatives (108 seats, compared to 83 for the Democrats, along with fifteen Senate seats (including the majority of those contested in that election). In other words, the Republicans began their existence not as a third party, or even a second party, but as the instantly dominant party on the ballot. The future “Grand Old Party” showed itself a Grand Young Party not only with its Congressional candidates, but with its first-ever Presidential nominee – John C. Fremont – in 1856. Rather than making the traditional, pointless and masturbatory third party gesture and winning 2% or 10%, Fremont made a real race of it against the Democrat James Buchanan: losing the popular vote 45% to 33%, and the electoral vote, 174 to 118. The real third party candidate was former President Fillmore, whose anti-immigrant Know Nothing campaign drew a few remnants of the Whigs and took just enough votes away from Fremont in New Jersey and Pennsylvania to give Buchanan narrow victories and the electoral majority. By the time they nominated Lincoln four years later, Republicans commanded clear majorities in nearly all the northern states and fully expected to sweep more than enough of those states (especially in light of Democratic divisions) to put him in the White House.
. In the pre-Civil War election of 1860, the Republicans hardly represented an upstart third party effort: they won a clear majority of 59% of the electoral vote and a comfortable plurality (40%) of the popular vote. The real “third party” in this election involved the Southern Democrats who abandoned their national nominee, Stephen A. Douglas, and campaigned for Vice President (and future Confederate general) John C. Breckinridge, winning 18% of the popular vote and 72 electoral votes. Meanwhile, former Cotton Whigs and pro-union Democrats from border states launched a fourth party campaign, winning 13% of the popular vote and 39 electoral votes for their man.”
Formed in 1854 and majority party in the Senate and Congress and President in 1860, never really a third party.
I disagree with Medved, but it is academic.