The answer is "No". Abraham Lincoln was a raging liberal by middle 19th Century standards. He wanted to end the conservative establishment of slavery and even took the nation to war to do so. The conservative establishment today (which is represented mainly by Republicans) would be in favor of continuing slavery, just as the conservative establishment represented mainly by Democrats in the 1860s wanted to continue the institution of slavery.
The Republican Party of the 1860s and in the decade afterward was undoubtably a "liberal" political party by modern political definitiions. They believed in using the power of the federal government to bring about dramatic change to end slavery and then to impose the will of the federal government on the Southern states during reconstruction. Much has changed in the Republican and Democratic parties since then.