WASHINGTON (AP) — After narrowly thwarting a youthful progressive upstart's primary challenge, veteran Rep. Henry Cuellar says his fellow Democrats greeted him on the House floor last week with one overwhelming sentiment: gratitude.

“If I would have lost, that would have created a wave of momentum against all the other Democrats” facing liberal challengers, said Cuellar, a 64-year-old Texan. “I can tell you, I've never been given so many thanks.”

Cuellar's Super Tuesday victory was among the year's first showdowns in which progressive challengers are trying to oust more moderate congressional Democrats, including several House committee chairs. Now, insurgent candidates face tests from New York to California, even as Joe Biden builds momentum in his race for the Democratic presidential nomination against independent Vermont Sen. Bernie Sanders, a self-avowed democratic socialist.

There’s no consensus over whether the former vice president‘s recent surge will translate to votes for incumbent Democrats trying to fend off progressive rivals. But with last week’s Super Tuesday contests handing liberal challengers a series of defeats sprinkled with glimmers of hope, most remaining insurgents face long odds.

“It means that we have a lot of work to do for infrastructure" that campaigns need like fundraising, said Alexandra Rojas, executive director of Justice Democrats. Rojas, whose progressive group recruited Alexandria Ocasio-Cortez to run in 2018, said while liberals are becoming a stronger political force, “I’m not going to pretend that it’s not going to be hard."

“An incumbent’s record of service, how they impacted the community, what is the last thing they’ve done for the voter, is always going to be top of mind over ideology,” said Dan Sena, a campaign consultant who ran House Democrats' political arm when they won control of the chamber in 2018.

Super Tuesday proved a tough day for progressives. Biden defeated Sanders in 10 of 14 states. Party-backed favorite MJ Hegar easily outperformed a progressive hopeful in Texas' Democratic Senate primary, though she still faces a May 26 runoff. In Southern California, liberal San Diego Councilwoman Georgette Gómez was hoping to make the November ballot, though she trailed a fellow Democrat in a partial vote count.

And then there's Cuellar, one of Congress' most conservative Democrats and a top target of Justice Democrats and Ocasio-Cortez's own political organization, Courage to Change. He defeated immigration lawyer Jessica Cisneros, 26, in the South Texas district, but by fewer than 2,800 votes, despite outspending her by over 2-to-1.

“The voters spoke, and they do want moderates in the Congress,” Cuellar said.

Many incumbents are taking heart from Biden's rising advantage over Sanders. Rep. William Lacy Clay, D-Mo., said Biden's expected strong showing in Tuesday's Missouri presidential primary bodes well for his August rematch in St. Louis against progressive Cori Bush, a nurse he easily defeated in 2018.

Citing Sanders' problems winning as much as 40% support against Biden in most national polls, Clay said of the Vermont lawmaker: “It tells you the revolution was not televised.”

Progressives say they've already pushed the Democratic agenda leftward on issues like expanded health care coverage and the minimum wage. And they say there are still primaries they can win, thanks to the Sanders excitement among young and some Hispanic voters.

It's always difficult to defeat House incumbents, who usually have vast funding and name-recognition advantages. Of 376 House members seeking reelection in 2018, just four primary challengers prevailed. That included Ocasio-Cortez, then an unknown 29-year-old who defeated Rep. Joe Crowley, who was viewed potentially as the next House speaker.

Perhaps progressives' best shot this year comes March 17, when eight-term Rep. Daniel Lipinski, D-Ill., faces Marie Newman in Chicago's liberal-leaning southern suburbs. Lipinski, an opponent of abortion rights, defeated Newman two years ago, but this year she's outraised him and has backing from Sanders, Massachusetts Sen. Elizabeth Warren and Chicago Mayor Mayor Lori Lightfoot.

Newman says Cuellar's Texas victory is irrelevant to her primary. “I’m in perfect alignment with my district," she said.

“We're in trouble if we don't win that one,” added Sean McElwee, who runs Data for Progress, a research organization for progressives.

Challengers are mounting a credible challenge against 16-term Rep. Eliot Engel, D-N.Y., chairman of the House Foreign Affairs Committee, who represents a racially diverse district in Westchester and the Bronx. Engel has raised $1.2 million — not a huge sum by New York City standards — and faces a June primary against rivals including middle school principal Jamaal Bowman, who has won endorsements from progressive groups.

Also in New York, liberals have uphill races to defeat House Judiciary Committee Chairman Jerrold Nadler and Oversight and Reform Committee Chairwoman Carolyn Maloney — both approaching three decades in Congress.

In New Mexico, attorney Teresa Leger Fernandez had a strong showing at last weekend's statewide Democratic convention that suggests she'll be a strong candidate for an open House seat in the state's north. Leger Fernandez, backed by Ocasio-Cortez, is still facing former CIA operative Valerie Plame in the June 2 primary.

In Columbus, Ohio, Rep. Joyce Beatty is vastly outspending liberal upstart Morgan Harper in a March 17 primary. Beatty says she's glad to not be running “on a socialist Justice Democrat ticket" like she says Harper is. Harper, an attorney, says she thinks she can benefit from the attention the party's presidential race is getting in the student-heavy district.

And in western Massachusetts, House Ways and Means Committee Chairman Richard Neal is being challenged by a local mayor, though Neal boasts a massive fundraising advantage.

Celinda Lake, a pollster working for Biden and some congressional incumbents, says the Democratic presidential and congressional primaries operate on separate political planes.

With Biden drawing African American voters to the polls and Sanders' appeal to the young, Lake says contenders in House and Senate primaries will “face new voters who don’t know them as well, so they better get out and communicate.”

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