The citizens of the new republic did not desire to become a U.S. state at that time.
Only a decade later, when the debt for their young republic became tooburdensome, did the Texian citizens decide to explore the possibility of U.S. statehood. Additionally, there was a resistance by many in the U.S who feared that any talk ofTexan annexation would further aggravate relations between the U.S. & Mexico (which did not official recognize the Republic of Texas) & could precipitate a war -which ultimately did occur in 1846.
The unorthodox annexation, by a "Joint Resolution of Congress" and approved by the Texas Congress, in 1845 effectively ended Texas' statusas its own nation & became the 28th state admitted to the Union.
Additionally, part of the Compromise of 1850 called for a significant amount of territory belonged tothe Republic of Texas to be ceded by the State for recompense of its republic-era debt which had been absorbed by the U.S. upon annexation as a state. It had long beenfeared by many Texians, that entrance into the United States would cause their geographically immense nation to be divided down into several small states. It was ensured, by theU.S. annexation resolution, that such division would not occur - unless desired by Texas itself - with provisions for up to five states to be created from said territory,which still exists today. Texans were appalled with the notion of losing so much territory by the Compromise of 1850 in exchange for their former debt, however it wasrespectfully accepted.
Thankfully, this unfortunate loss created new state boundaries: establishment of the proudly unique & globally-recognized present-day SHAPE OF TEXAS!