House Budget Committee Chairman Paul Ryan (R-Wis.) and Senate Budget Committee Chairman Patty Murray (D-Wash.) on Capitol Hill. (Melina Mara/The Washington Post)

Lawmakers opened formal negotiations over the budget Wednesday by pledging to work across party lines to fund federal agencies, avoid another government shutdown and adopt lasting changes to rein in the rising national debt.

But the sudden outbreak of bipartisan bonhomie masked a lingering dispute over the issue of taxes, which looms once again as the biggest roadblock on the path to compromise.

Chastened by three years of budget showdowns and economic near-calamities, the 22 senators and seven House members on a new budget conference committee expressed fresh eagerness to end the era of government by crisis. Democrats, for instance, said they are ready to swap sharp but temporary cuts to federal agencies, known as the sequester, for permanent “structural changes” to federal health programs long sought by Republicans.

“I’m ready to make some tough concessions to get a deal,” said Senate Budget Committee Chairman Patty Murray (D-Wash.), the lead negotiator for Senate Democrats.

“But compromise runs both ways,” Murray warned. “Republicans are also going to have to work with us to scour the bloated tax code and close some wasteful tax loopholes and special interest subsidies, because it is unfair and unacceptable to ask seniors and families to bear this burden alone.”

Budget expert Stan Collender discusses what lies ahead for the budget conference committee. (The Washington Post)

Republicans, however, appear unwilling to make that trade, even with the sequester poised to slice another $20 billion from the Pentagon in January.

Rep. Tom Cole (R-Okla.), a member of the conference committee and a close ally of House Speaker John A. Boehner (R-Ohio), repeated his assertion that higher tax “revenue ought to be on the table.” But Cole limited his suggestions to such GOP-friendly ideas as selling off federal assets and giving corporations incentives to bring profits back home from overseas — a far cry from the assault on big-business tax breaks Democrats envision.

Meanwhile, House Budget Committee Chairman Paul Ryan (R-Wis.), the lead negotiator for House Republicans, said tax loopholes should be closed only in the context of comprehensive tax reform, so the money raised could be given back to taxpayers in the form of lower rates.

“Our tax code is full of carve-outs and kickbacks. We need to get rid of them. And bipartisan talks [over tax reform] are just the way to do it,” Ryan said.

The budget talks, on the other hand, should be limited to cutting spending “in a smarter way,” Ryan said. He added, “If this conference becomes an argument about taxes, we’re not going to get anywhere.”

The back and forth over taxes is just the latest version of the battle Republicans and Democrats have been fighting since the GOP took control of the House in 2011 on a promise to rein in the national debt, which was then spiraling out of control.

Since then, a series of budget deals — and an improving economy — have dramatically slowed federal borrowing. On Wednesday, the White House budget office announced that the government recorded a $680­ billion deficit in the fiscal year that ended in September, less than half the size of the shortfall President Obama inherited in 2009 when measured as a percentage of the economy.

Plummeting deficits have sapped urgency from the push for a so-called “grand bargain” to tame the debt through sharply higher taxes and significant cuts to federal health and retirement programs. So when lawmakers cut a deal this month to end a 16-day government shutdown and raise the federal debt limit, they agreed to appoint a budget conference committee to focus primarily on replacing the sequester cuts and keeping the government open past Jan. 15, when the latest government funding bill is set to expire.

Republicans, who took the blame in public opinion polls for the shutdown, are particularly eager to avoid another one. People involved in the talks say a deal could involve as little as $100 billion in alternative policies to replace a portion of the sequester for the next two years.

Senior Democratic aides acknowledge that most of the savings are likely to come in the form of spending cuts. But if Democrats are going to agree to cuts in Medicare benefits — for example, by charging wealthy seniors more — they argue that Republicans must agree, in the interest of fairness, to give up at least one tax break for business.

“Why would we reform Medicare and not consider scaling back tax breaks for Exxon Mobil?” Sen. Timothy M. Kaine (D-Va.) said during Wednesday’s meeting at the Capitol.

Most senior Republicans, however, remain unwilling to sacrifice even one tax benefit in the name of bipartisan compromise, arguing that higher taxes cannot solve the problem of soaring health and retirement spending.

Sen. Charles E. Grassley (R-Iowa) was particularly emphatic. “I will not entertain a so-called balanced plan that punishes small businesses and job creators with higher taxes,” he said.

Some Republicans hold out hope that the White House may be willing to do a deal without any tax increases. Obama himself suggested as much during a meeting with Senate Republicans during the shutdown, GOP senators said. And senior administration officials seemed to drop similar hints in recent public statements that listed replacing the sequester and making new investments in job creation as the administration’s top priorities.

Obama wants a deal “that has balance and is good for our economy. Everything should be on the table in these talks,” White House spokeswoman Amy Brundage said Wednesday via e-mail.

If Democrats insist on raising taxes, Ryan and other GOP leaders, including Senate Minority Leader Mitch McConnell (R-Ky.), have said they will simply let the sequester stay in place. But that strategy is likely to raise the risk of a shutdown in January and a fresh crisis over the debt limit later in the spring — which may explain why Cole is working hard to keep the door to taxes open.

“You can find revenue without raising taxes,” he said Wednesday. “Let’s leave a little helpful ambiguity in what I’m saying.”