The debate over whether to raise the legal limit on government borrowing has riveted Americans, with a large majority worried about the potential consequences regardless of whether Congress votes to allow the national debt to keep increasing.

But when pressed to name their biggest concern, nearly half of respondents say they are alarmed by the prospect that the debt could grow beyond its current limit of $14.3 trillion, according to a new Washington Post-Pew Research Center poll. Only 35 percent say they are more worried about the risk of default and economic destabilization if Congress does not raise the debt limit.

The poll vividly illustrates the dilemma facing lawmakers as they approach an Aug. 2 deadline on the debt ceiling. While congressional leaders in both parties have acknowledged that the Treasury needs to keep borrowing to pay the government’s bills, lawmakers are likely to face voters’ wrath if they can’t prove that they are also working to rein in the spiraling debt.

On Tuesday, Vice President Biden emerged from a fourth round of debt-reduction talks with six lawmakers from both parties and announced that the group is on pace to reach an agreement on more than $1 trillion in spending cuts, part of a package aimed at smoothing passage of a debt-limit increase.

“I think we’re in a position where we’ll be able to get to well above $1 trillion [in cuts] pretty quick,” Biden told reporters after meeting with lawmakers for 21 / 2 hours at the Capitol.

The group agreed earlier this month to look more closely at proposed cuts, worth nearly $200 billion over the next decade, to a variety of programs. On Tuesday, it dove into the more contentious question of whether to cut Medicare and Medicaid, the biggest drivers of future borrowing — a top GOP priority. In return, however, Biden said he will insist that Republicans back down on their opposition to new taxes.

“Revenues are going to have to be in the deal,” he said.

House Majority Whip Eric Cantor (Va.), one of two Republicans in the talks, reitereated the GOP opposition to tax increases.

“This process shows that if people come together, finding spending cuts isn’t that hard,” Cantor said. But, he said, “tax increases cannot pass the House.”

House GOP leaders, meanwhile, scheduled a vote for next week on a measure to raise the debt ceiling by $2.4 trillion without an accompanying debt-reduction package, a move intended to show that such legislation has no chance of passing. Speaker John A. Boehner (R-Ohio) has said that any debt-limit increase must be paired with a package of spending cuts that equals or exceeds the amount by which the debt ceiling is raised.

“They have nothing to sell right now,” said Republican consultant Tony Fratto, who as a Treasury Department official in the George W. Bush administration helped press Congress to push up the debt limit six times. Fratto said that while he believes the debt limit should be raised, without conditions, to avoid turmoil in financial markets, that position is clearly not acceptable to a majority of Americans.

“They need to get to a credible number on spending cuts,” Fratto said. “Once they get to a product to sell, it will be a challenge. But I think they will be able to convince people that voting for the debt ceiling was a beneficial exchange.”

For now, a wide swath of the public remains confused about the debt-limit debate, with nearly half — 48 percent — saying they don’t understand the consequences of congressional inaction. Half of those surveyed say they do have a good grasp of the consequences, however, and that knowledge appears to affect their opinion about whether Congress should act.

Among those who believe they are well-informed, 52 percent say they worry more about Congress raising the limit and permitting additional borrowing. By comparison, 37 percent worry more about the possibility of default. Those who consider themselves less well-informed are more evenly split, with 45 percent more worried about borrowing and 34 percent more concerned about default.

The partisan divides are even more dramatic. Republicans are more than twice as likely — 60 percent to 25 percent — to say their bigger fear is that raising the debt limit would lead to more spending. Democrats split 48 percent to 38 percent the other way, with default as their greater concern.

Independents — crucial to the reelection prospects of as many as a dozen Senate Democrats, as well as President Obama — tend to side with Republicans. Among independents, 49 percent say they worry more about additional debt, while 34 percent say their bigger fear is the risk of default.

“Republicans cannot support a debt-limit increase that does not have major spending cuts. The base won’t allow it,” said GOP pollster Glen Bolger, noting that independents wouldn’t like it, either. “The challenge for the House — and the Senate and the president, as well — is how do they come up with something where people think we’re taking a step forward rather than just two steps back.”

The Washington Post-Pew Research Center poll was conducted by conventional phones and cellphones from May 19 to 22 and included interviews with 1,004 adults. The full poll has a margin of sampling error of plus or minus 3.5 percentage points.

Staff writer Felicia Sonmez contributed to this report.