The quick answer is no, but the detailed answer is "it depends on what the house outlet is, and how far it is from the trailer." Running just the AC is doable off a 20A circuit with a short run of heavy-duty cord. Few household outlets are 20A, however... those are generally single-outlet "dedicated appliance" outlets, such as one for a deep freeze or spare refrigerator in the garage. 20A double-gang outlets are common, but usually used in light commercial rather than residential settings, just because 15A is a little cheaper and that's how most homes are wired.
*IF* you have a 20A outlet, make sure it's really on a 20A circuit and not something that was just wired onto a 15A circuit with a bunch of other outlets on it. Measure the voltage with the AC off and monitor the voltage with the AC on. If the voltage drops below 110 with the AC running, you're likely to damage it over time. Also watch for your cords and connectors getting hot.
The best solution for running the AC is to have a dedicated 30A 120V RV circuit, but that takes time and money.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill