Since the end of the Civil War, there have been continuous grumblings about secession coming out of Texas. The truth is, since their own war of independence with Mexico the idea of a Texas Republic has been strong in the state. Just 16 years after annexation they wanted to leave the union, and our Civil War was their opportunity because Texas, unlike the other southern states had far more reason to leave. The "States Rights" stance of the Lincoln federal government at the time clashed not only with the southern way of life, but specifically with many of the stipulations in the Texas Treaty of Annexation. Forced back into the union after 4 years of war and fear of another Mexican invasion, and over 600,000 American deaths, the Texans of that time never truly wanted to be American. The loyalty of the average Texan was to their state first, and then to the union.
Today however, Texas has become deeply woven into our ideas of what America is. It's in the heart of the country, and much of the world that otherwise knows nothing of our culture would recognize an image of the classic American cowboy. Texas, as big as it is, actually needs the union far more than the union needs it despite the fist-pounding of local politicians and Tea Partiers. So what would happen to a new Republic of Texas?
First and foremost, articles of secession would need to be drafted and approved by a majority of the population. Should that happen, the federal government would need to recognize it and NOT intervene militarily. Considering almost all of our military bases have been in the south since the end of the Civil War as part of the occupation, it would be difficult for a Texas militia or conscripted army to win, even with the support of neighboring states or the entire south. Our military is drawn from all over the country and the individual soldier has no loyalty to the state they find themselves stationed in, and wouldn't mutiny as locally-drawn forces may have, had a successful secession happened just 75 years ago.
Assuming Texas did manage to leave peacefully or by force, all of the federal programs the citizens had become accustomed to would halt and they would immediately lose U.S. citizenship. No more Social Security. No more Medicaid. No federal highway maintenance, no PEL grants, no small business subsidies, NOTHING that has the word "federal" in it would apply to any citizen of the new Republic. This alone would alienate any infirm person who relied on medicaid and social security and would be a catastrophe for the elderly population whose only source of income and healthcare would immediately halt.
The rest of the population would no longer have FDIC insurance on their savings and would need to begin trading in a new Texan currency as the Republic would have no right to print U.S. Dollars. The ensuing run on the local banks would cause such turmoil that most of them would go belly-up almost immediately as a new currency would have little value on the international market. Anyone with any sense would try and rescue their Dollars as quickly as they could and would be reluctant to convert to the new currency.
The borders would immediately be closed, and citizens of the new Republic would need to obtain passports to enter the United States proper. New trade deals would need to be hammered out between Texas and the rest of the world, the U.S. included, and luckily for the new Republic, they have a considerable coastline. Sea trade would be possible but tariffs due upon passing through U.S. waters and crossing our borders would make it difficult to profit from any such initiatives. Closed borders would halt all products from entering or leaving Texas for a time and this would further weaken their new currency as the scarcity of numerous materials and products would lead to price gouging and terrible inflation.
Once the banking catastrophe gets sorted out, and the republic begins collecting taxes that had once been going to the fed, they could begin setting up their own programs but would be unable to pay for things like Social Security. Texas and other southern states have long enjoyed an income from the federal government, with Texas taking in over $40 Billion in federal funding in 2011 alone. This money would no longer be there and estimates for starting just the most important social programs comparable to what the U.S. currently offers would top a trillion dollars. Add to this the cost of funding a military and buying it's own equipment, either from the U.S. or Russia, and the new Republic would be deficit spending for decades. They would have no credit on international markets and no one would be willing to loan the country any money at all, which, of course, would continue to devalue its currency.
Finally, there are the social ramifications. With the Texas vote gone, Democrats would dominate elections in the U.S., quickly taking over the House, Senate and the presidency, while in the new Republic of Texas, religious conservatism would take hold. Christian values would spread into government unchecked and would be codified into law with no interference from that pesky U.S. constitution and watchdog groups like the ACLU. The U.S. would begin looking far more like Canada and Texas would begin looking far more like Mexico as they'd lack the funding to secure their own border. Economically and socially isolated, we may end up with a religious state as bad as Iran on our southern border, in constant conflict with Mexican drug lords and their own increasing Latin population.
Secession would be everything Texas never wanted.