Essentially, what happened in your scenario is this.
1. State governments, including that in the South, gain more resources and authority to police their own population, which empowered landed "aristocracy" (quotes because they didn't have titles, but they were aristocracy for any other meaning), without federal oversight. So, legalization branch of state governements is firmly in control of wealthy and prestigeous families, and therefore the control of Senate is under control of said families. (17th Amendment, which established that senators should be elected, was passed in 1913, to fix this problem exactly). By suppression of voters, Representatives would most likely also under landed aristocracy, so they have full control of Congress. Which also means control over Supreme Court.
2. Then this people, who are in control of Senate and, generally, are religious, established some kind of state religion clause to the Constitution. The first attempt to do so, as far as I know, happened in 1863, but it failed. Still, in your scenario, the control of the Congress is given to people who want it, so yeah, something like that - "We, the people of the United States, humbly acknowledging Almighty God as the source of all authority and power in civil government, the Lord Jesus Christ as the Ruler among the nations, His revealed will as the supreme law of the land, in order to constitute a Christian government, and in order to form a more perfect union, establish justice, insure domestic tranquillity, provide for the common defense, promote the general welfare, and secure the inalienable rights and the blessings of life, liberty, and the pursuit of happiness to ourselves and our posterity, and all the people, do ordain and establish this Constitution for the United States of America." - can pass Congress. It wouldn't change lifes of people who could vote anyways, so your opposition would be people who oppose this kind of things in a matter of principle; you can't have a revolt by the people like that.
3. Then federals institued FBI and prosecuted hard all political opposition to the said aristocracy block.
4. When Senate offered a title to the President, there was no organized power that could oppose it. Local public that could rise up were suppressed by both local police and FBI, leaders are imprisoned and/or assassinated.
5. Then federal elections, which are meaningless to this point anyways, are abolished.
I'd say 10 years is indeed too fast, but 15-20 years, yeah, that's possible in the environment of 1830s-1850s.