By Nicole Gaudiano and Chuck Raasch

You know a new level of cooperation has been achieved when conservative GOP Rep. Jason Chaffetz of Utah shares pizza and hosts a telephone town hall with liberal Democratic Rep. Peter Welch of Vermont.

Such odd pairings are springing from a small but growing coalition in Congress that wants an immediate end to the war in Afghanistan.

"We both saw that by working together ... we could be more effective," Welch said Tuesday in his office before he and Chaffetz teamed up on the call to Vermont constituents.

The two have joined forces on a measure to withdraw all troops from Afghanistan, except those involved in counter-terrorism operations.

"I think we see it very similarly," said Chaffetz, sitting at a small table beside Welch.

Can such unlikely matchups -- which have formed not just around the war but on issues ranging from education to the Patriot Act -- serve as templates for the emotional debate over the federal debt and deficit?

Don't count on it.

"As long as he agrees with me, we'll be fine," Chaffetz said, smiling.

He arrived at Welch's office just minutes after voting with Republicans and 82 Democrats against a bill to raise the debt ceiling without also cutting spending.

Welch voted in favor of the bill.

"There's some issues where we are miles apart," he said. "But where we're together, then let's work something out."

Welch said he doesn't know if his collaboration with Chaffetz on Afghanistan signifies a chance for broader agreement.

"But I think if we're going to have any chance of being successful, both sides have to acknowledge that it's going to require us to find common ground," he said.

Welch is a member of the liberal Congressional Progressive Caucus. The fiscally conservative Chaffetz, who may run for Senate, counts Utah tea party members among his supporters.

The two came together in May on a letter urging President Barack Obama to pull out of Afghanistan and change U.S. anti-terrorism policy.

Highlighting the cost of the war -- $2 billion weekly and $386 billion already spent -- Welch, Chaffetz and a bipartisan group of six other lawmakers called for a shift in strategy from "nation building" to one modeled after the successful mission that located and killed terrorist Osama bin Laden.

During their phone call with Vermont constituents, Welch and Chaffetz referred to nation-building and "mission creep" in faulting the war strategy.

The same issue has drawn together veteran antiwar liberals such as Rep. Dennis Kucinich of Ohio and Rep. Barbara Lee of California with presidential candidate Rep. Ron Paul, R-Texas, former Alaska Gov. Sarah Palin, and Rep. Walter Jones, R-N.C., a former Democrat who originally supported the wars in Iraq and Afghanistan.

Rep. Dana Rohrabacher, R-Calif., one of the most fiscally conservative members of the House, cut short a news conference in March to vote for an end-the-Afghanistan-war proposal by Kucinich. That proposal failed after drawing 93 favorable votes, including eight from Republicans.

But the similar measure that Welch and Chaffetz proposed last month got more votes -- 123, including 18 Republicans. Welch also co-sponsored a measure to require a plan for turning over military operations to Afghan authorities. That proposal got 204 votes, including 26 from Republicans.

Both measures failed, but the growing support is significant, Welch said.

"These votes have given President Obama an enormous amount of latitude to accelerate and intensify a withdrawal," he said. "What he's heard loud and clear from Congress is that if he orders a substantial drawdown, he'll get support, not criticism."

Chaffetz has similar views. He said he just needs to convince his colleagues it's OK, as conservatives, to vote to bring troops home.

"It's the longest war in the history of the United States," he said. "It's hardly 'cut and run.'"