As the Senate prepares to begin next week to craft legislation that would curb gun violence, Sen. Dianne Feinstein declared confidence that the Senate would pass her proposal to reinstate and significantly expand the federal ban on assault weapons.

Appearing on CNN’s “State of the Union” to discuss her bill, which she introduced last week with Rep. Carolyn McCarthy, D-N.Y., the California Democrat conceded to host Candy Crowley that she faced a big challenge.

“This has always been an uphill fight,” said Feinstein, who sponsored the previous assault weapons ban that was in effect from 1994 to 2004. “This has always been the hardest of the hard.”

But Feinstein added that she had a strategy for ensuring a vote on her bill, which this time would have no sunset date.

Feinstein’s bill would, among other things, bar the future sale, transfer, manufacture and importation of 157 specific kinds of semiautomatic guns and impose the same restrictions on ammunition magazines that contain more than 10 rounds. It would also simplify the definition of an assault weapon by reducing the number of defining physical characteristics from two to one, making it more difficult for gun manufacturers to define firearms that elude the ban.

Feinstein told CBS’ “Face the Nation” host Bob Schieffer that she had made a concession by not requiring that current owners of military-style weapons register their firearms. “I would like to see them all registered, but it’s not in our bill,” she said.

As the second most senior member on the Judiciary Committee behind Chairman Patrick J. Leahy, D-Vt., Feinstein will have considerable influence in including her bill’s provisions in any comprehensive measure the panel puts together, she said.

“I have been assured by the majority I’d be able to [offer] it [as an] amendment on the floor, which is what I did in 1993,” Feinstein told CNN.

Many lawmakers, Senate Majority Leader Harry Reid, D-Nev., among them, have said that any overhaul of the current gun laws would have to be “comprehensive” in order to pass both chambers. The overhaul, sparked by the massacre at Sandy Hook Elementary School in Newtown, Conn., would also have to pass a certain amount of muster with the powerful National Rifle Association and the lawmakers who support the organization’s interests.

John Gramlich contributed to this report.