If “Meet the Press” moderator David Gregory were a guest on his own show, he knows the kinds of questions he’d be asked.

Why have your ratings been falling? Is the show in trouble? Is your job in trouble?

“I get it,” says Gregory, the face of the longest-running TV program in American history (founded: 1947). “Do I want to be number one in the ratings? Every week I want to be number one, and we fight like hell to get there. And it’s tough right now. It’s a fight.”

He adds, “I’m not just trying to sell you — well, I am trying to sell you — but I’m not going to B.S. you, either. Yeah, it’s hard. I see what our challenges are. But we’re going to fix our problems.”

The main problem: The great-granddaddy of Sunday-morning Beltway blabfests isn’t just not No. 1. It’s No. 3 and in the midst of a three-year slide. During the first three months of this year, the NBC program finished behind perennial rivals “Face the Nation” on CBS and “This Week With George Stephanopoulos” on ABC, despite being helped by two weeks of Winter Olympics hoopla. In the final quarter of last year, viewing among people ages 25 to 54, the preferred group for TV news advertisers, fell to its lowest level ever.

Bad enough. But fairly or not, Gregory’s “Meet the Press” still gets measured against the lofty peaks scaled by Tim Russert, his predecessor. Russert, the folksy inquisitor, ruled the ratings for more than a decade until his death in June 2008. He often attracted an audience 40 percent larger than his rivals, an unheard-of margin in television.

But now — to paraphrase Russert’s famous sign-off — if it’s Sunday, it’s not necessarily “Meet the Press” that Americans are watching.

These days, the leader is “Face the Nation,” hosted by Bob Schieffer, the grandfatherly 77-year-old newsman. Schieffer not only attracts the largest overall audience (a weekly average of 3.35 million during the first three months of 2014, 5 percent more than “This Week,” 8 percent more than “MTP” and 61 percent more than “Fox News Sunday”) but the largest audience among the coveted 25-to-54 set, too. (Schieffer’s competitors are quick to point out that comparisons aren’t quite fair since “FTN’s” ratings are based on its first half-hour, not the standard full hour; the program’s second half-hour isn’t broadcast by CBS stations in many cities).

The Sunday shows — which comprise what Schieffer calls “the smartest morning on TV” — are more than just prestige projects for the networks; the relatively large and affluent audiences they attract make them magnets for corporate image advertisers that pay premium prices for airtime. Russert’s dominating position helped NBC earn a reported $60 million from “Meet the Press” in 2007.

Thus, “MTP’s” meltdown has sounded alarm bells inside NBC News and attracted the attention of its new president, Deborah Turness, who arrived from Britain’s ITV News in August. Gregory’s job does not appear to be in any immediate jeopardy, but there are plenty of signs of concern.

Last year, the network undertook an unusual assessment of the 43-year-old journalist, commissioning a psychological consultant to interview his friends and even his wife. The idea, according to a network spokeswoman, Meghan Pianta, was “to get perspective and insight from people who know him best.” But the research project struck some at NBC as odd, given that Gregory has been employed there for nearly 20 years.

Around the same time, the network appointed a new executive producer at “MTP,” Rob Yarin, a veteran media consultant. Yarin, who had worked with Gregory on an MSNBC show, “Race for the White House,” during the 2008 campaign, succeeded Betsy Fischer Martin, who reigned over “MTP” for 11 years. Fischer Martin had helped Russert soar to glory, but had disagreed with Gregory over matters of style and substance (she was promoted to oversee all of NBC’s political coverage).

In interviews, Yarin and Gregory say they are tinkering with the show to keep it abreast of a changing media environment. They’ve made the program’s pacing faster, with shorter interview segments. The range of topics and interview subjects has been opened up, too. Last month, for example, Gregory interviewed NCAA President Mark Emmert about proposals to unionize student-athletes — stealing a little thunder, he notes, from CBS, which was televising the NCAA basketball tournament at the time.

The overall effect is that the program now bears only a vague resemblance to the one over which Russert presided. Whereas Russert would spend multiple segments grilling a single newsmaker, Gregory now barely goes more than six or seven minutes on any interview or topic.

The changes were readily apparent on Sunday’s program, recorded at NBC’s studios in Northwest Washington. After opening with Gregory’s taped interview with Ukrainian Prime Minister Arseniy Yatsenyuk, the host moved swiftly to live dual-screen chats with Senate Foreign Relations Committee members Bob Corker (R-Tenn.) and Chris Murphy (D-Conn.). Then it was on to the journalists’ roundtable discussion, followed by an interview with Democratic National Committee chair Rep. Debbie Wasserman Schultz (D-Fla.) about health care and the midterm elections.

Then, still more segments: A new recorded feature called “Meeting America” in which reporter Kevin Tibbles looks at something happening outside Washington (in this case, a debate in Kentucky over the building of a Biblical theme park using tax subsidies); more roundtable discussion; and a photos-of-the-week feature called “Images to Remember.” The program closed with a short interview with New York Times reporter Jo Becker about her new book about gay marriage, “Forcing the Spring.”

Gregory says the new look “delivers on the core of what ‘Meet the Press’ is” but “widens the aperture . . . I’m dedicated to building something that says we’re not just thinking about politics. We’re thinking about who the real influencers are in this country.”

“This Week,” which is anchored irregularly by Stephanopoulos (he also hosts the daily “Good Morning America”), says it’s shaking things up, too.

The ABC program has a new executive producer, Jonathan Greenberger, a 30-year-old Stephanopoulos protege. Greenberger started at ABC News out of college at 22, and climbed so fast that the network waited for him to finish Stanford Law School before handing him the executive producer job at “This Week” last year.

Greenberger describes a program that is more ensemble in nature and more of a magazine than a traditional newsmaker-interview show. On a recent program, Stephanopoulos chatted with an ABC reporter in Ukraine about the latest news, then segued to a discussion with correspondent (and sometime fill-in host) Martha Raddatz about the unfolding diplomacy, followed by an interview with Samantha Power, the U.S. ambassador to the United Nations.

“A few years ago, we wouldn’t have moved so fast to integrate all of those elements into the program,” says Greenberger. “We’d have the vice chairman and chairman of the Foreign Relations Committee on to have a debate.”

Like “Meet the Press,” “This Week” has to be wary of changing too much. The ABC program is still recovering from its attempt to build itself around former CNN correspondent Christiane Amanpour, whose strength is foreign affairs, not domestic politics. Amanpour lasted about 18 months as host before going back to CNN in 2011.

Schieffer, meanwhile, says “Face the Nation” isn’t planning to change. “There’s no bells and whistles here,” says the host, who’s been “Face’s” face since 1991. “We just try to move the stories of the week forward.”

The good news for all three shows is that they remain among the most durable on TV, if perhaps less influential than they once were. Even as everything else on TV has lost viewers over time, the Big Three have held steady and even gained viewers. Collectively, about 9.6 million people watched them each week during the first three months of this year, about the same number that watched Russert in 2005. This doesn’t count the audience for innumerable Sunday-morning competitors, from Fox News Sunday (hosted by former “Meet the Press” moderator Chris Wallace) to “Al Punto” on Univision.

The shows can occasionally make news, too, if the interview subject is big enough. Conservatives are still raising questions about then-United Nations ambassador Susan Rice’s comments on the Sunday shows in 2012 about the attack on a U.S. facility in Benghazi, Libya that left four Americans dead. Gregory, meanwhile, mentions his “Meet the Press” interview with Vice President Biden in 2012, in which Biden expressed support for same-sex marriage, prompting President Obama to become the first sitting president to declare his support a few days later (in an interview with ABC).

Gregory himself has sparked controversy for what he’s said and done on the air. Conservatives called for the moderator’s prosecution after he held up a high-capacity ammunition magazine in an interview with National Rifle Association chief executive Wayne LaPierre in late 2012 (possession of such armaments is illegal in the District; Gregory wasn’t charged). Last June, the Twittersphere exploded with outrage when Gregory asked journalist Glenn Greenwald about having “aided and abetted” NSA secrets leaker Edward Snowden, insinuating that Greenwald was complicit in espionage.

The impossible burden for Gregory, of course, has been to follow the beloved Russert. As one NBC colleague describes it, Russert is a “ghost” who still haunts Gregory’s tenure at “MTP” six years into his run.

“I am fully aware that there are a lot of people who believe Tim Russert will never be replaced, and I’ve never tried to replace Tim Russert," he says. “I have nothing but respect and admiration for Tim and his legacy. And I’m doing my own thing, just like Tim did.”

But he also adds, a little more defensively, “I’ve covered the White House, I’ve covered 9/11, the road to war, constitutional crises, and honestly, I wouldn’t be able to focus on this job if I was going to let that stuff get to me. I knew it would be there going in and I’m just focused on being David Gregory and taking the show to the next level.”

Some Gregory supporters think he has the best hand to play over the long haul. Stephanopoulos has already pulled back from moderating “This Week” and may be in line to succeed 68-year-old Diane Sawyer as the anchor of “ABC World News Tonight” some day. Although Schieffer says he hasn’t set his retirement date, it may be not be very far way — “another year or so,” as he put it.

Which means both CBS and ABC would have to retool their Sunday-morning shows with new moderators.

“Time is on David’s side,” says Bloomberg View columnist Jeffrey Goldberg, a semi-regular “MTP” panelist. “It’s semi-inevitable. He just has to keep doing what he’s doing, and continue to break new ground on the big stories of the week. In five to 10 years, we’ll be talking about him as the grand old man of Sunday morning.”