Lawmakers in both parties are urging President Obama to offer a detailed plan for curbing the national debt in the speech he is to deliver Wednesday, warning that they will not authorize fresh borrowing unless he agrees to mandatory restraints on future spending.

With the debt nudging closer to the legal limit — set at $14.3 trillion — anxiety is running high on Capitol Hill. Lawmakers are reluctant to approve legislation that would permit the debt to rise or to face the potentially devastating economic consequences if the government were to stop borrowing and default on its obligations.

Just to see the nation through next year, lawmakers would have to raise the limit by nearly $2.2 trillion under the spending plan Obama submitted to Congress in February, according to congressional budget analysts. Even the austere blueprint that House Republicans plan to approve this week would require about $1.9 trillion in fresh debt by October 2012 — a month before the next presidential election.

Republicans and Democrats alike said Tuesday that failing to raise the debt limit would invite catastrophe. But many said they could not in good conscience authorize more borrowing unless Obama agreed to cap federal spending, adopt triggers to force rewrites of the tax code and entitlement programs, or accept some other binding mechanism for bringing the debt under control.

“We’re going to require as a condition for raising the debt ceiling something really important,” Senate Minority Leader Mitch McConnell (R-Ky.) told reporters. “That means no window dressing, no blue smoke and mirrors — something real, something measurable that clearly will begin to reduce our debt.”

Sen. Joseph I. Lieberman (I-Conn.) said: “It’s not just Republicans. A lot of Democrats, including myself, are not going to vote to raise the national debt ceiling unless there is something concrete, real, tough done to guarantee that the debt itself will be reduced in the coming years.”

McConnell said he will “be talking to the president about that very subject in great detail in the coming weeks.” He and other congressional leaders are scheduled to meet with Obama at the White House on Wednesday morning to preview the president’s speech, as Washington turns from the narrow battle over 2011 spending cuts to the more profound debate about how to shape an affordable government for an aging society.

The White House said Obama’s afternoon speech will lay out four steps to controlling spending without undermining the economy – keeping domestic spending low, finding new cuts in the defense budget, reducing health-care costs and boosting tax revenues.

Obama will also invoke elements of his 2012 budget and borrow from recommendations made by the bipartisan fiscal commission, a White House official said. He will say reductions in health-care spending should be accompanied by an effort to improve Medicare and Medicaid.

“The president will make clear that while we all share the goal of reducing our deficit and putting our nation back on a fiscally responsible path, his vision is one where we can live within our means without putting burdens on the middle class and seniors or impeding our ability to invest in our future,” a White House official said.

White House officials have adamantly rejected the idea of including spending caps or other budget-process reforms in legislation to raise the debt ceiling, arguing that ensuring the government’s solvency is too important to be held hostage to other issues.

On Tuesday, White House press secretary Jay Carney affirmed the administration’s position. Obama is not expected to alter it in the speech, which he is scheduled to deliver at George Washington University.

“We don’t believe . . . that there should be a link between efforts to address our long-term deficit problem and debt problem and the imperative of raising the debt ceiling,” Carney said. The White House, he added, fully expects Congress to acquiesce to the administration’s request to raise the limit “because everyone recognizes the consequences of not doing it, which would be to throw the global economy into chaos.”

Congressional authority to limit federal borrowing dates to the founding of the republic. According to the Congressional Research Service, Congress authorized every federal loan until 1917, when it agreed to set an overall ceiling to give the Treasury more flexibility as the nation entered World War I.

Raising the debt ceiling is usually a perfunctory matter. Congress has raised it at least nine times since 2001. The bills usually prompt partisan posturing about fiscal responsibility but little real drama. This time is different because the debt has climbed to its highest point, compared with the size of the economy, in more than 50 years. And there’s no end in sight without a major tax increase or sharp cuts to popular safety-net programs for retirees.

With world financial markets still jumpy from the recent recession and anxious about the growing load of government debt in a host of countries, many lawmakers worry about giving the perception that the United States lacks the political will to manage its finances — especially after the display of partisan brinksmanship over 2011 spending that nearly forced a government shutdown last week.

“We cannot go through the same process on the debt limit. Default would be unspeakably cataclysmic. Getting close to default would be unspeakably cataclysmic,” said Senate Finance Committee Chairman Max Baucus (D-Mont.), who is working to develop a “balanced” mechanism for restraining spending and raising revenue that would be acceptable to both parties. “We’re acting like we don’t know how to run the country. And that is not a good perception to leave.”

With the debt expected to hit the ceiling by May 16, Treasury Secretary Timothy F. Geithner said he can take measures to push the deadline to July 8. Republican leaders made clear Tuesday that they plan to use the extra time.

McConnell said the Senate is likely to consider a debt limit measure “between Memorial Day and the Fourth of July.” And House Majority Leader Eric Cantor (R-Va.) predicted another protracted negotiation as Republicans and Democrats battle over whether to impose legal limits on spending, precisely where to set spending targets or caps, and what the legal consequences would be if those terms were breached.

“I suspect, given what happened last week, we’re going to be in a struggle,” Cantor said. “We’re going to be in a robust debate with this White House.”

There are a handful of proposals on the table, including a bipartisan plan to establish a “glide path” to lower overall spending over the next decade from 24 percent of the economy to the historic average of 20.6 percent of the gross domestic product. If Congress failed to meet the annual caps, the White House would be required to cut spending across the board.

But Baucus said Democrats will not accept caps on spending unless Republicans agree to a similar mechanism to raise taxes.

Meanwhile, Senate Budget Committee Chairman Kent Conrad (D-N.D.) said he wants to see a much more comprehensive plan that commits Congress to a detailed strategy for raising taxes, overhauling entitlement programs and cutting spending that would knock projected borrowing back from about $9 trillion over the next decade under the president’s budget blueprint to a more economically manageable $5 trillion.

Conrad is a member of the bipartisan Gang of Six senators, which is working to develop such a plan, modeled on recommendations of Obama’s fiscal commission. Obama, too, is using the commission’s work as the foundation for his entry into the suddenly more sober debate over government borrowing.