The easiest way for Sam Houston to be president of the US is for a deadlocked Democratic convention in 1852 to turn to him. Unlikely, but unlikelier things have happened with deadlocked conventions. If nominated, he would almost certainly win, the Whigs being terribly divided on the slavery issue. And his presidency would be interesting, because he is the only possible Democratic nominee in 1852 I could think of who definitely would *not* support the Kansas-Nebraska bill as president.
it is also just barely conceivable he could have become president in 1860 if (a) the Constiutonal Unionists had nominated him instead of Bell, and if (b) the race had gone to the House, and if (c) the Republicans in the House, seeing that they could not get Lincoln elected there, threw their support to Houston. (IMO all three conditions are unlikely. To confine myself to (a), Houston was too much of an Old Democrat for a party that was mostly a party of Old Whigs, and he was also hurt by his advocacy of a US protectorate over northern Mexico.)
However, both these scenarios depend on Texas having been annexed. There is no way Houston could *simultaneously* be president of the US and of an independent Republic of Texas. He had sworn allegiance to the United States of Mexico in 1835 and thereby lost his US citizenship. (One could argue that he had already lost it by accepting citizenship in the Cherokee nation--but the Supreme Court would hold in 1831 that the Cherokee nation was not sovereign.) Later of course he was a citizen of the Republic of Texas. He did not regain his US citizenship until Texas was annexed. Since he was now once again a US citizen, and, because he had been born in the US, a "natural born" one, he was now eligible for the US presidency.