AUSTIN — Democrats in key Texas House races are gambling that voters are so outraged over Child Protective Services' failings, they'll blame incumbent Republicans.

CPS' woeful failures to move promptly in Dallas and Houston child abuse cases — including its dawdling and botched investigation just weeks before the March beating death of 4-year-old Leiliana Wright of Grand Prairie — have become a marquee issue in at least three closely watched state representative races.

In recent days, Democratic challengers and allied groups have launched cable TV ads, online videos and mailers that try to link Dallas County GOP Reps. Rodney Anderson and Kenneth Sheets and Rick Galindo of San Antonio to the state agency's woes.

The ads claim the three GOP House members have shortchanged Texas children and cloaked CPS' needs for more money and caseworkers.

The incumbents have dismissed the attacks as misleading, unfair and a sign of their opponents' growing desperation.

Rice University political scientist Mark Jones said the Democrats' tack on CPS is an attempt to woo swing voters, mostly whites — many of them women.

"It's a pretty compelling message," he said. "The ads link the suffering of children to insufficient resources at CPS, which links back to Republicans not sufficiently increasing the budget for CPS."

State GOP leaders have vociferously denied they've underfunded CPS, noting cash infusions that date to a big overhaul of the agency pushed by Gov. Rick Perry in 2005.

In interviews, Sheets and Anderson emphasized that the Legislature increased CPS funding by $231 million last session and is poised for an even bigger increase next year.

Last week, Lt. Gov. Dan Patrick said in a written statement that since the 2005 session, CPS has had an 85 percent increase in funding to reach its current two-year level of $2.85 billion.

But liberal budget expert Eva DeLuna Castro of the Center for Public Policy Priorities said Texas still lags most states, including most Southern states, in what it spends to shield kids from abuse and neglect. In fiscal 2014, Texas spent only $188 per child on child protection, compared with a U.S. average of $391 per child, she said.

"Yes, we have put in more money," DeLuna Castro said. "But our child population has grown rapidly. We are still spending a lot less than most states — about half of the U.S. average per child."

Ads and mailers from the GOP incumbents' opponents and their allies cite recent stories in The Dallas Morning News. The newspaper has reported that tens of thousands of Texas children believed to be in imminent danger of abuse or neglect were not being seen promptly by CPS child abuse investigators — and thousands had not been checked at all.

They also refer to last year's votes by Sheets, Anderson and Galindo against a budget amendment that would have required CPS' parent agency to study and recommend minimum and maximum caseloads.

"If you could help save children's lives with one vote ... what would you do?" says a mailer supporting former Democratic Rep. Philip Cortez in a San Antonio rematch against Galindo.

The mailer highlights the amendment, which failed along party lines by a vote of 99-43.

"It was a common-sense measure: examine the Department from head-to-toe, to see what's working and what's not. ... This was Rick Galindo's chance to help, but he voted 'NO.' "

The Democratic group Lone Star Project created online ads attacking Anderson and Sheets, whose opponent is Victoria Neave of Garland, for votes that "blocked research to reduce CPS caseloads and help save kids' lives."

A cable TV ad supporting Democrat Terry Meza of Irving in her race against Anderson was paid for by the liberal political action group Annie's List. In the ad, images flash across the screen of headlines and text taken from coverage of CPS' failure to protect Leiliana, whose investigative caseworker had a staggering 70 open cases.

A female narrator says Leiliana was "choked, beaten, thrown into a closet — left for dead. ... Rodney Anderson voted no, throwing the truth into the closet."

Anderson said the ad was over the line.

"To say that voting against a study, I might as well have thrown her in the closet, is patently absurd," he said. Speaking of Meza and her Democratic supporters, he said the ad "just shows the depth of desperation they will go."

Sheets said for him, the criticism is distressing. He and his wife, Michele, have adopted two children who were in CPS custody, he noted.

"Foster [care] issues are important for me, and to level such an attack against us, it's just dishonest and it's disgusting," he said.

The caseload study proposed by Houston Democratic Rep. Armando Walle was "a showboat amendment," Sheets said.

"Why would we spend that money for a report when we have a report from The Stephen Group that's just been completed and a report from the Sunset Commission?" he said, referring to a consultant's study and an advisory group's report. Both reaffirmed a need for better training and time management at the department, he said.

"We didn't need to study this issue. We need to take action," Sheets said.

But Democratic consultant Jeff Cosby, who helped design some of the hit pieces, said voters are the ones who are disgusted — with tightfisted GOP lawmakers who proclaim they love children and then act to the contrary.

"They've been trying to ignore the problems at CPS for a long time," he said of Republican leaders. "This scandal didn't just land in their lap yesterday."

Rice's Jones said the Democrats' ads "are stretching things a little bit." But they are an apt "metaphor for broader Republican opposition to substantial budget increases for CPS," he said.

"It's not a fair and balanced ad. But then, negative attack ads are never fair and balanced," he said.

Democrats hold only 50 seats in the 150-member chamber.

They appear to be targeting the three GOP incumbents in hopes of picking up five or six seats this year, Jones said.

Staff writer Hannah Wise in Dallas contributed to this report.