WASHINGTON (AP) ― Just days before the Senate begins debating new gun control measures supported by President Barack Obama, the Democratic senator who is leading the push to restore an assault weapons ban acknowledged on Sunday that the effort faces tough odds to pass Congress but has public support.

Sen. Dianne Feinstein of California told CBS television’s “Face the Nation” that a coalition of police, clergy and voters would push forward her gun control measure over objections from the nation’s largest gun-rights lobbying group, the National Rifle Association.

Feinstein 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 reelection might fear pro-gun voters and the NRA.

“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 to raise large amounts of money to defeat lawmakers who support gun control. She said the NRA has become 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.

The Senate Judiciary Committee plans to take up the gun control proposals on Wednesday and hear testimony from the NRA’s CEO and senior vice president, Wayne LaPierre. Mark Kelly, the husband of former Rep. Gabby Giffords, who was wounded in a 2011 mass shooting that killed six in Tucson, Arizona, plans to testify in support of gun control laws.

Rep. Paul Ryan of Wisconsin, the Republican vice presidential nominee in 2012, said Congress should focus on the causes of violence and not the weapons alone.

“We need to look beyond just recycling failed policies of the past. ... Let’s go beyond just this debate and make sure we get deeper. What’s our policy on mental illness? What’s going on in our culture that produces this kind of thing? You know, we need to have that kind of a discussion and debate,” Ryan said.

In the wake of the school shooting in Newtown, Connecticut, Obama is pushing for universal background checks on gun purchasers, restoring the assault weapons ban and banning high-capacity ammunition magazines.

Obama’s proposals drew support from thousands of people, many holding signs with the names of gun violence victims and messages such as “Ban Assault Weapons Now,” taking part in a rally for gun control on Saturday in the U.S. capital.

Leading the crowd were marchers with ``We Are Sandy Hook’’ signs, paying tribute to victims of the December elementary school shooting in Newtown, Connecticut. Washington Mayor Vincent Gray and other city officials marched alongside them. The crowd stretched for at least two blocks along Constitution Avenue.

Participants held signs reading “Gun Control Now” and “What Would Jesus Pack?” among other messages.

About 100 residents from Newtown, where a gunman killed 20 students and six educators, traveled to Washington together, organizers said.

Education Secretary Arne Duncan told the crowd it’s not about taking away gun rights guaranteed by the U.S. Constitution’s Second Amendment, but about gun safety and saving lives.

“This is about trying to create a climate in which our children can grow up free of fear,” Duncan said. “This march is a starting point; it is not an ending point ... We must act, we must act, we must act.”

But in the Senate, some of Obama’s fellow Democrats may frustrate his efforts to enact the most sweeping gun control measures in decades. These Democrats from largely rural states with strong gun cultures view Obama’s proposals warily and have not committed to supporting them.

All eyes are on these dozen or so Democrats, some of whom face re-election in 2014. That includes Sens. Max Baucus of Montana, Mark Begich of Alaska and Mark Pryor of Arkansas.

In an interview for the Feb. 11 edition of The New Republic magazine, Obama said that gun-control advocates have to do a little more listening than they do sometimes in the debate over firearms.

“Part of being able to move this forward is understanding the reality of guns in urban areas are very different from the realities of guns in rural areas,” he said.

The president says it’s understandable that people are protective of their family traditions when it comes to hunting.

“So it’s trying to bridge those gaps that I think is going to be part of the biggest task over the next several months. And that means that advocates of gun control have to do a little more listening than they do sometimes,” he said.

Even before Obama announced his gun proposals earlier this month, Senate Majority Leader Harry Reid told a Nevada television station that an assault weapons ban would have a hard time getting through Congress.

Feinstein’s original assault weapons ban was a stern political lesson for Democrats. Its passage as part of President Bill Clinton’s crime bill in 1994 was blamed for Democratic election losses that year after the NRA campaigned against lawmakers who supported the legislation. When the assault weapons ban came up for renewal in 2004, Congress, under pressure from the NRA, refused to extend it.

Reid has pledged action on gun measures. “This is an issue we’re not going to run from,” he said. But he’s under pressure from all sides.

The NRA, known for rewarding friends and punishing enemies, promises it will be closely watching Reid in the upcoming gun control debate.

The NRA generally opposes legislation mandating universal background checks and disputes gun control groups’ claims that 40 percent of purchases happen without such checks. NRA officials question whether background checks could be done effectively in a way that makes a difference and doesn’t disrupt legitimate sales.