Seward was not trusted by Greeley, Phillips, Lovejoy, and the radicals of their complexion. They apprehended that after using the "American citizens of African descent," until he (Seward) should be safely seated in the Presidential chair, he would abandon the negro and "Tylerize" their Party; hence, they would not trust him
Source: wiktionary
"The great doctrine of equal rights will prevail," wrote Medill, of the Chicago "Tribune," to President Johnson in September, 1865, warning him not to Tylerize his party nor go back on those who had elected him.
Source: wiktionary
Thus to Tylerize became a term meaning to forsake the party to which one owes allegiance or office.
Source: wiktionary