1828, "ostentatious display," American English, of uncertain origin; originally among the class of words considered characteristic of "Western" (i.e. Kentucky) dialect. Perhaps a blend of splash and surge. The meaning "extravagant indulgence in spending" is first recorded 1928.
"to make an ostentatious display, to put on a splurge" (in the older sense of the noun), by 1843, from splurge (n.). Thornton's "American Glossary" has an 1848 citation defining splurge (v.) as "to expatiate at large, to appeal to broad and general principles." Meaning "to spend extravagantly" is by 1934. Related: Splurged; splurging.