Im going to start with a brief history of Texas so I can shed a better light on the whole annexation issue.

In the early days of Texas when it was still a Mexican territory the residents were overwhelmingly settlers from the United States or Tejanos (Mexicans born in Texas).

Stephen F. Austin had been invited by the Mexican Government to bring American settlers to the sparsely populated territory. The allure of cheap and plentiful land attracted many people from the Southern US to settle in Texas. With the acknowledgement that they would be relatively free to run their own affairs (which included Slavery).

This arrangement was fine for awhile, but after the abolition of slavery in 1829 in Mexico, the settlers became rather unruly so in 1830 the government passed an act that prevented further immigration from the US, raised taxes, enforced other unfair rules and also reinforced the abolition of slavery. This was seen in paramount to the policies that Great Briton had forced on the colonies in the 1760s-1770s.

Things stayed hot for awhile, but not yet quite rebellious until 1834. When General Santa Anna toppled the government in a coup and made himself dictator. And in doing so in 1834 replaced the Constitution. This to many Texans was the final straw. They saw all of their rights being stripped away that they had seen as theirs from the Constitution of 1824 (to be fair to the Mexicans though, many of them were appalled as well and there was talk of revolution in Mexico itself not just in Texas).

In 1835 the revolution started and Texas won. Many wanted to be just straight annexed by the United States. However many also felt that since they had just won their Independence they should be their own country. Yet there were many issues preventing outright annexation. The US would basically be starting a war with Mexico if it did. And even though Mexico had tongue-in-cheek accepted and acknowledged Texas Independence it wasn't that simple. Santa Anna and the Mexican Government still considered Texas apart of Mexico and wouldn't just let the US take it over. They barley even tolerated Texas Independence.

The first President of Texas Sam Houston was a great fried of the US President Andrew Jackson. Yet Jackson wouldn't even recognize Texas as a nation until his last day in office. The reason why was even more complicated than just making Mexico upset. One of Texas conditions on joining was that it could be split into several states if it so choose. This in effect could add several new slave states into the Union upsetting the already fragile balance between slave state and free. Also there was the issue involving Texas debt but this was considered a minor issue. In 1837 when Memucan Hunt, Jr. presented an offer of annexation to the US President Van Buren outright rejected it sighting the Slavery issue and political caution. Further proposels of annextation were sent to the US Congress but both houses either voted it down or filibustered it. Finally in 1838 the staunchly independent minded Mirabeau B. Lamar was elected President of Texas and withdrew all proposals of annexation from the US.

As you can see the way the people and government in Texas felt about annexation shifted either way at various times. The contention among many is that Texas had always set out to join the Union.

A majority of the population was from the United States, they held the same ideals and values, as well as language and culture, further they formed a government with a primary goal being annexation by the US.

Yet later ideas and feelings shifted to Texas remaining independent. A National identity had been formed during the revolution and the years afterwords.

So in summary and a direct answer to your question is that; Texas intended to be annexed by the US from the start of the revolution but later ideas and opinions shifted to remaining independent.

There are so many more avenues and figures to discuss about Texas Annexation. But I figured Id just give a brief overview. I suggest if you want to know more look up the any of the books Ive listed in the sources below. Or heck even go read the Texas annexation documents and treaties of the US Government or Texas archives websites.

Sources - The Texas Revolution and the U.S.–Mexican War A Concise History. Jefferson, NC: McFarland.

Eighteen Minutes: The Battle of San Jacinto and the Texas Independence Campaign. Plano, TX: Republic of Texas Press.

Texas: All Hail the Mighty State. Archie P. McDonald. Austin, TX: Eakin Press.

Slavery and the Annexation of Texas https://books.google.com/books?id=yOEBAAAAMAAJ&printsec=frontcover#v=onepage&q&f=false

Related question:

During the decade that Texas was independent, I'm assuming they made treaties with local Indian tribes as well as trade agreements with other states. What happened to these when Texas was annexed? Were they reworked or were simply discarded?

As a follow up question because I have tried asking this as a question of its own and it's never answered: When and How did the Republic of Texas establish diplomatic relations with the Republic of Yucatan? I know there were embassies in Merida and Houston (?) and there were naval battles in which the two young republics fought together against the federal mexican navy but I can't find how these relations were established.