The Republic Of Texas (1836-1845) was in a sense sustainable, but in other regards it wasn't. Let's get some starting context first about the Texan economy of the time. The Texan economy was so far in debt and over-inflated because of the Texan Revolutionary War that it faced serious economic woes. In Sam Houston's first administration as the president of Texas, the public debt had from approximately $1,250,000 to $3,250,000. The second president of Texas, Mirabeau B. Lamar had pushed the debt even further by around $4,855,000 or so to the public debt. However the United States had been granting large loans to the Republic. The biggest problem Texas faced was arguably its inflated currency, also known as "Redbacks"

Had the war been cheaper on the new nation, perhaps the economy could of been better off. Around the time of annexation, the Texan economy had begun to heal as the income had begun equalling its expenditures. During the days of the Republic, Texas hadn't a incorporated or public banking system but there were plans for a quite large banking institution. Had Sam Houston focused on creating a banking system in Texas the economy could of likely been much better. The Republic Of Texas could of been sustainable if it was given another 20 years due to its natural resources such as its abundance of cattle, wheat, cotton, and salt just to mention a few. Infact, Texas is one of the leading salt producers in the country. Another factor that would of helped Texas get back on its feet was the rise of the railroad, which was gaining traction in the late 40s. Had Texas stayed independent for just some time more, it could of been a sustainable nation.

If you need to check my sources, you can find some of my information which I said on the Texas State Historical Association.