Well, this the first thread on this topic that made it to a second page without degenerating into a bunch of macho posturing. A few comments.
1. Texas is not the only state to be a republic upon admission to the Union. Vermont was a self-governing republic (January 15,1777-March 3, 1791) despite land claims from New York and New Hampshire. It provided independent military units during the Revolutionary War (the famed "Green Mountain Boys" under Ethan Allen), and was never effectively organized by any of the claimants. the Vermont Republic also established a mint and issued it's own coinage.
In 1779, John Greenleaf Whittier anonymously published "The Song of the Vermonters" which had characteristics in the last stanza that were similar to Ethan Allen's prose and caused it to be attributed to Allen for nearly 60 years. The last stanza reads:
Come York or come Hampshire, come traitors or knaves,
If ye rule o'er our land ye shall rule o'er our graves;
Our vow is recordedour banner unfurled,
In the name of Vermont we defy all the world!
The Vermont Constitution of June 2, 1777 outlawed slavery and extended adult male sufferage to all regardless of property ownership; the first entity to do either in North America. BEFORE being admitted to the Union, Vermont agreed to pay to New York 30,000 Spanish milled dollars in settlement of New York's claims (more on this later).
2. Texas was admitted to the Union as a result of an Act of Congress ratifying a treaty with the Republic of Texas. Texas was allowed to bypass the territorial phase by submitting its state constitution for Congressional approval while independent. That constitution, as noted by another poster was approved and took effect December 29, 1845. The other poster is in error, however, in confusing that constitution as the organic act. The organic act was the United States Act of Congress authorizing the Treaty of Annexation and that Treaty.
3. The treaty did not resolve the borders of Texas and left the Texas Republic's debt of $10 million the responsibility of the State of Texas. It soon became obvious that Texas could not pay this debt. One of the components of the "Compromise" of 1850 was a bill through which the United States assumed the debt and Texas agreed to its present boundaries. Unlike Vermont, it turns out that Texas historically was never able to fund itself or its land claims.
4. As noted, the Articles of Confederation explicitly forbade the right to succeed.
5. In Lincoln's First Inaugural Address you will find the best constitutional analysis of the issue of succession. Lincoln begins with an argument that sovereignty implies a perpetual union.
Lincoln's First Inaugural Address said:
I hold that in contemplation of universal law and of the Constitution the Union of these States is perpetual. Perpetuity is implied, if not expressed, in the fundamental law of all national governments. It is safe to assert that no government proper ever had a provision in its organic law for its own termination.
Then Lincoln progresses to a second point; if the United States is a voluntary compact, the law of contracts must apply.
Lincoln's First Inaugural Address said:
If the United States be not a government proper, but an association of States in the nature of contract merely, can it, as a contract, be peaceably unmade by less than all the parties who made it? One party to a contract may violate itbreak it, so to speakbut does it not require all to lawfully rescind it?
Thirdly Lincoln makes an historical argument about the nature of the Union, which predates the Constitution.
Fourthly Lincoln makes a basic point about the law of nations. A successful revolution is its own justification. A failed revolution is just treason.
Lincoln's First Inaugural Address said:
This country, with its institutions, belongs to the people who inhabit it. Whenever they shall grow weary of the existing Government, they can exercise their constitutional right of amending it or their revolutionary right to dismember or overthrow it.
He closes this point by noting that no one has an oath to destroy the Union, but he has taken an Oath to preserve it.
Lincoln's First Inaugural Address said:
You have no oath registered in heaven to destroy the Government, while I shall have the most solemn one to "preserve, protect, and defend it."
I'll avoid quotations and detail, but in the Address Lincoln also makes several practical arguments that the South was better off inside the Union than outside it, that the doctrine of succession would devolve into anarchy, and that the protection of slavery was more viable with a federal government than some treaty between North and South as sovereign nations. It is in the South's best interest to remain in the Union.
Following a discussion of the Supreme Court, Lincoln refrains from endorsing the Crittenden Amendment, while saying that if passed he would abide by it, and indicates a constitutional convention of delegates elected by the people (and who could not be officeholders in state or national government!) to propose any amendments.
Lincoln closes with the famous appeal to the shared history as a nation.
I am frankly puzzled that most discussions of succession ignore this speech. Not only is it historically important, but it is a pinnacle of constitutional reasoning and an astounding triumph of rhetoric.