Three plants operate in the United States, with the meat exported.
The bill is now less likely to pass after the US House Agriculture Committee attached several amendments that are unlikely to win wide support.
They include a requirement for a programme in New York or Kentucky to take in potentially thousands of unwanted horses. The amendments also require the federal government to pay agistment for the horses, and compensation horse owners who can no longer sell a horse for processing for human consumption.
Supporters and detractors appear to hold entrenched positions. Supporters of the bill argue that slaughter for human consumption is cruel and should not be allowed to occur in the United States, where horses played such a pivotal role in the country's history.
Detractors argue that slaughter is more humane than having horses starve to death at the hands of owners who no longer want to care for them.