By Dan Gilgoff, CNN.com Religion Editor

(CNN) – As it organizes Catholic watch parties for Thursday night’s debate between Joe Biden and Paul Ryan, who are both Roman Catholic, the Obama campaign hasn’t been shy about suggesting that the GOP vice presidential nominee hasn’t lived up to his Catholic values.

“For Catholic outreach, a defining moment in this campaign has been (Mitt) Romney’s selection of Paul Ryan as his running mate,” said Broderick Johnson, a senior adviser with Barack Obama’s campaign who spearheads Catholic outreach efforts.

“The Ryan budget has entered into quite a debate, particularly among Catholics, in terms of the moral test and what is in that budget and what the budget proposes to slash.”

Johnson is referring to the proposed budget that Ryan crafted in his role as chairman of the House Budget Committee, which was roundly criticized by many Catholic interests – including by the Catholic bishops – for cutting programs that help the poor.

The Obama camp hopes the debate will provide an opportunity to reprise such Catholic criticisms of Ryan. “The vice presidential debate will be a significant event and will provide a strong contrast on how these two men from the same faith come to two different visions for the country,” said Michael Wear, Obama's national faith vote coordinator.

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For a party that has often been accused of insufficient piety by its Republican and conservative opponents, Democrats' implications that the GOP vice presidential nominee has fallen short of his Catholic faith are a dramatic turnabout.

And it’s not the only way the Obama campaign and liberal groups are using Thursday’s debate to organize Catholic voters, one of the country’s big swing voting constituencies.

Beyond encouraging Catholic watch parties, the Obama campaign has been visiting Catholic colleges in swing states and dispatching Catholic campaign surrogates to address Catholic groups in the leadup to the debate.

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“Every time I see the president, we talk about how Catholic outreach is going,” Johnson said. “He’s very interested in that, and it makes my job more meaningful.”

Left-leaning Catholic groups that aren’t officially connected to the Obama campaign have been even more vocal in attacking Ryan from a Catholic perspective.

“Some of his positions are fundamentally at odds with the teachings of the Catholic Church,” said a Ryan critique issued this week by dozens of Catholic theologians and other Catholic scholars.

The organizers of the statement, part of a group called On All of Our Shoulders, said that while Catholic politicians who support abortion rights are often called out for their differences with their church, “Catholic Republicans who dissent from church teaching on issues such as torture, war, the environment and the economy receive far less scrutiny.”

With Ryan, progressive Catholic groups have taken particular aim his proposed budget, which passed the House but not the Senate.

A letter to Ryan from faculty at Georgetown, a Catholic university, summed up the Catholic opposition to the proposal: “We would be remiss in our duty to you and our students if we did not challenge your continuing misuse of Catholic teaching to defend a budget plan that decimates food programs for struggling families, radically weakens protections for the elderly and sick, and gives more tax breaks to the wealthiest few.”

This year, a group of progressive nuns organized a “nuns on the bus tour” to decry what it called the Ryan budget’s “slashing of programs for the poor.”

This week, the nuns reprised the tour, criss-crossing Ohio just in time for the vice presidential debate. “He clearly has not been where I’ve been," Simon Campbell, an organizer of the tour, told MSNBC of Ryan. “He just is out of touch.”

A progressive group called Catholics United is organizing watch parties for the debate, noting in an e-mail blast to supporters that the event marks the first time two Catholics vying for the White House are facing off.

“This election is coming down to the wire and the Catholic vote will certainly play an important role in determining who will win,” the group said.

The Romney campaign, like the Obama campaign, has rolled out a Catholic outreach effort. And Ryan has invoked his Catholic faith on the campaign trail after defending his budget in distinctly Catholic terms earlier in the year.

“The work I do, as a Catholic holding office, conforms to the social doctrine as best I can make of it,” Ryan said in an April speech at Georgetown in which he responded to criticism of his budget.

Ryan has promoted the Catholic idea of “subsidiarity,” which he says means that “the government closest to the people governs best” and which he says informs his budget proposal.

When Romney introduced Paul as his running mate over the summer, the Republican presidential hopeful called him “a faithful Catholic” who “believes in the worth and dignity of every human life.”

About one in four American voters is Catholic, though there is such a broad range in Catholic political concerns and voting habits that many political experts reject the notion of a cohesive Catholic bloc.

Catholics have voted with the winning presidential candidate in every election since the early 1990s.

In 2008, Obama beat John McCain among Catholics by 54% to 45%. In 2004, John Kerry – the first Catholic nominee for president since John F. Kennedy – lost the Catholic vote to George W. Bush, provoking Democrats to take Catholic outreach more seriously.

Both major parties had America’s highest-profile Catholic cleric, New York Archbishop Timothy Dolan, give the closing prayer at their recent political conventions.

–CNN’s Dan Merica contributed to this report.