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WASHINGTON—Sen. Dianne Feinstein, who’s leading the push to restore an assault weapon ban, acknowledged on Sunday that the effort faces tough odds to pass Congress and she blamed the nation’s largest gun-rights group.

Feinstein, D-Calif., on Thursday introduced a bill that would prohibit 157 specific weapons and ammunition magazines that have more than 10 rounds. The White House and fellow Democrats are skeptical the measure is going anywhere, given lawmakers who are looking toward re-election might fear pro-gun voters and the National Rifle Association.

“This has always been an uphill fight. This has never been easy. This is the hardest of the hard,” Feinstein said.

“I think I can get it passed because the American people are very much for it,” Feinstein said of the measure that follows a similar measure she championed into law 1994 but expired a decade later.

She acknowledged, however, the NRA’s political clout. “They come after you. They put together large amounts of money to defeat you,” Feinstein said. She also said the group was a pawn of those who make weapons. “The NRA is venal. ... The NRA has become an institution of gun manufacturers,” she said. The NRA disputed her characterization. “The NRA is a grass-roots organization. We have more than 4 million dues-paying members and tens of millions of supporters all across this country. Our political power comes from them. Decent and logical people would understand that,” spokesman Andrew Arulanandam said.