Two bipartisan groups of lawmakers are stepping up efforts this week to reach a deal on raising the nation’s $14.3 trillion debt limit, now set to expire on Aug. 2. So far, neither has been able to make any significant headway on the fundamental ideological difference that divides them – whether to raise taxes or cut spending – but a vote scheduled for Tuesday could offer at least a glimpse of compromise.

Vice President Joe Biden and a half dozen negotiators tapped by House and Senate leaders from both parties will meet three times this week starting Tuesday – an increase from biweekly meetings. The group says it will keep up the new pace until a deal is reached.

On a parallel track, five members of the bipartisan Gang of Six, minus Sen. Tom Coburn (R) of Oklahoma, are pushing to complete their own plan, which aims to cut $4.7 trillion in deficits during the next 10 years. But if they don’t come to terms soon, their efforts will be “irrelevant,” says Sen. Kent Conrad (D) of North Dakota, a member of the Gang of Six and chair of the Senate Budget Committee.

Both teams are struggling because their Democratic and Republican negotiators disagree about how the economy works. The pressures of the coming presidential campaign season, which tend to impose a partisan template on all decisions, are only exacerbating the problem.

“The Republicans think that cutting taxes is the way to improve the economy and the Democrats believe that spending is the way to improve the economy,” says Peter Wallison, a former White House counsel in the Reagan administration, now at the American Enterprise Institute.

“These are differences that need to be bridged, and they are black and white,” he adds.

Offsetting the debt-limit increase – but how?

The debate over the debt limit is framed by House Speaker John Boehner (R) of Ohio's insistence that any increase in the debt limit must be counterbalanced by by an equal amount of spending cuts. Estimates suggest adding $2.4 trillion to the debt ceiling would carry Congress to the end of 2012.

Sen. Jon Kyl (R) of Arizona, a member of the Biden group, says his party will insist on $2.4 trillion in "real savings," but suggests that he is open to some flexibility on the timing of those spending cuts. “Spending reductions could play out over a decade or more,” Senator Kyl told reporters on June 7.

Another member of the Biden talks, House majority leader Eric Cantor (R) of Virginia, says that there’s a chance this week to build momentum toward a deal. He credits Vice President Biden with a willingness to put all issues on the table.

“He is conducting these meetings in a way that has kept the ball rolling,” he said, adding that the group is “well in sight of over $1 trillion in spending cuts.”

But tax increases are off the table, he adds. “I won’t support tax increases because the House won’t support them,” he told reporters in a briefing on Monday.

In a break with this GOP anti-tax orthodoxy, however, Senator Coburn is bringing an amendment to the Senate floor on Tuesday that aims to end $6 billion in tax breaks for blenders of ethanol. If his bid is successful, it could signal GOP support for cutting tax breaks as a tool for reducing deficits.

Groups such as Americans for Tax Reform view the Coburn move as a tax increase that violates the group's taxpayer pledge, unless there are other net tax cuts to compensate for eliminating a tax break. In a nod to that standard, Sen. Jim DeMint (R) of South Carolina said on Friday that he will propose an amendment that both eliminates the ethanol tax break and ends the estate tax.

Important Tuesday vote

But in a potentially important development, another powerful conservative group, the Club for Growth, is backing the Coburn amendment regardless of what happens with the DeMint amendment. The Club for Growth has even announced that it will include Tuesday’s Senate vote in its annual scoring of legislators – meaning that it will mark down legislators who don't vote for the bill.

“Senator Coburn has always been an ally of the pro-growth cause,” says spokesman Barney Keller.

Democrats are watching Tuesday’s vote closely as a signal of a break in GOP ranks that could help resolve the debt negotiations.

“Picture a herd of wildebeest facing a river of crocodiles,” says one Democratic senator. Breaking with the partisan herd on taxes is perilous. “But if you can get a few to break out of the pack – and if they make it through the crocodiles to the other side – the others will come,” the senator said, speaking not for attribution.

Negotiators on both sides of the aisle say that there is a heightened sense of urgency this week to resolve the debt crisis before financial markets react.

“We don’t want the market to make these decisions for us,” said House majority leader Cantor on Monday.

If Congress raises the debt ceiling without serious spending cuts and entitlement reforms, “interest rates will skyrocket, and there will be no way for us to see any return to growth anytime soon," he said. "We will have to raise taxes and the rest. No one wants that.”