The legislation is aimed at shutting down three processing plants but time is running out this year, with Congress set to adjourn at the weekend.
It would also ban the transporting of horses for slaughter, meaning they could not be taken out of the country for this purpose.
However, the bill, which is waiting to go before the Senate, may not make it, with several senators indicating they would block any attempts to have the matter heard before next year.
The industry is worth US$60 million a year, with much of the meat being exported for human consumption in Europe and Japan.
The US plants slaughtered more than 90,000 horses in 2005.