Two weeks before their final deadline, President Barack Obama and top lawmakers will face more pressure Tuesday for a debt deal amid a growing sense that a last-ditch plan taking shape in Congress may be the only way to avoid a devastating U.S. default.

With talks at an impasse and time growing short for raising the U.S. debt ceiling, attention will shift to a congressional vote on a Republican deficit-cutting measure seen as mostly symbolic but a stark reminder of their ideological divide with Obama's Democrats.

More important than Tuesday's political theater will be any progress behind-the-scenes on a fallback option that would give Obama almost all the authority — and the blame — for raising the $14.3 trillion debt limit before the government runs out of money to pay its bills on Aug. 2.

The stalemate in Washington, along with debt problems in Europe, is unnerving financial markets worldwide amid fears of a spiral into a global crisis, and the situation could worsen unless a U.S. deal is struck soon.

While insisting Obama has not given up on forging far-reaching $4 trillion deficit-reduction deal, the White House has finally signaled that a broader plan may be out of reach — something many in Washington accepted days ago.

"We must pursue a fallback or last-ditch option ... Conversations about that have been ongoing," White House spokesman Jay Carney told reporters.

With no word of new talks planned between Obama and congressional leaders, a solution that has gained traction is one based on a proposal by Republican Senate Minority Leader Mitch McConnell originally envisioned as "Plan B" if all else failed. He has been talking to Senate Democratic leader Harry Reid about revising it to try to win bipartisan support.

Before moving forward, Republican leaders are insisting on votes they hope will soothe fiscally conservative Tea Party members and score political points with the public -- but which also could clear the way for compromise with Obama.

SCORING POINTS

Republicans who control the House of Representatives will push for a measure to cut and cap spending and amend the U.S. Constitution to require a balanced budget even though Obama has already promised to veto it should Congress pass it.

The vote on Tuesday gives Republicans a chance to argue the need for deep spending cuts. That could give House Speaker John Boehner, reluctant to see his Republicans blamed for a debt default, the political cover to pursue a deal that includes less-dramatic spending cuts than his party has so far sought.

Failure to meet the Aug. 2 deadline for raising the debt ceiling could cause tumult in global markets and push the United States back into recession. Jitters over the impasse contributed to declines in U.S. and world stocks and a jump in gold prices to record highs on Monday.

Reid accused Republicans of "playing a game of political chicken" with the global economy.

House Republican Majority Leader Eric Cantor chided Obama for threatening to veto the "cut, cap and balance" proposal.

McConnell's convoluted plan for avoiding default would dump the task into Obama's lap by authorizing him to raise the debt ceiling in three stages before the November 2012 election. Such a move would spare Republicans from having to explicitly back an increase in the U.S. borrowing authority.

McConnell has said he wants to make Obama a one-term president. His proposal could shift any blame for increasing the debt burden to Obama in a campaign season when the president is seeking re-election from voters increasingly concerned about ballooning deficits.

But many conservative Republicans in the House oppose McConnell's plan as a political maneuver that would not put the brakes on spending.

Also with an eye to the elections, Reid wants to show that Democrats favor spending cuts as well, by adding roughly $1.5 trillion in cuts to the plan, which would include creation of a special bipartisan deficit-reduction committee.

Obama had indicated earlier that a deal on lifting the debt limit was needed by July 22 to leave time to write and approve legislation. But Carney said that was not a "hard deadline," though the two sides needed to "move the ball down the field this week" to ensure an agreement by next week.