Curbelo will cosponsor the bill with Seth Moulton, a Democrat from MA.
"We're going to look at the issue", Goodlatte told the Washington Post.
House Speaker Paul Ryan says easing taxes on manufacturers and other businesses is critical to helping America remain competitive in an increasingly global economy.
"I think it's appropriate and in his interest to move on to the next chapter of his life", Ryan said, adding that he won't go into the "timing" of the resignation.
The ATF said in 2010 that it did not believe bump stocks to be regulated under existing gun laws because it is a firearm part. Florida Sen. Bill Nelson is a co-sponsor of the bill.More news: Steven Smith returns home with injury, David Warner to lead
The devices, originally meant to help people with disabilities, fit over the stock and grip of a semi-automatic rifle and allow the weapon to fire continuously, some 400 to 800 rounds in a single minute.
"Automatic weapons are banned in our country and this device converts semiautomatic weapons into automatic weapons that can fire up to 800 rounds per minute", Curbelo said on "Varney & Co".
Ryan said that even though he's an avid hunter, he had never heard of the devices before Sunday's mass shooting in Las Vegas.
"A lot of us are coming up to speed with just what this is, but having said that, fully automatic weapons have been outlawed for many, many years", Ryan said during the conference. "Fully automatic weapons have been banned for a long time". Ileana Ros-Lehtinen, R-Miami, Gus Bilirakis, R-Palm Harbor, both said they would support Curbelo's bill.
He said he's received calls from "dozens" of his House Republican colleagues but declined to say how many would sign on and said he hoped to introduce it sometime on Thursday. Republican governors John Kasich of OH and Charlie Baker of MA also came out this week as backing a prohibition on bump fire stocks with Baker going so far as saying he would sign such a bill "tomorrow" if it was sent to him by lawmakers. His approach mirrors a measure introduced by House Democrats on Wednesday. "It's obvious that this is a flagrant circumvention of the law, and no member of Congress should support any circumvention of existing law".