Nikki Haley is pitching voters on policies that recall an era when the Republican Party stood for a fiscal conscience and foreign policy leadership, at a time when the most sacred of federal programs and the international alliances that built the post-World War II era are under enormous strain.

But the voice of contemporary Republican politics, Donald J. Trump, has been there to attack those appeals virtually ever day. On Tuesday, the voters of New Hampshire may decide whether the party can find a path back from Mr. Trump’s big government domestic policy and his isolationism abroad.

Ms. Haley’s proposals to raise the retirement age for young workers and trim benefits for the wealthy while protecting Social Security and Medicare benefits for those at or near retirement may sound familiar to voters with any historical memory. They’re the essentially same plans pitched by Mitt Romney and his running mate Paul D. Ryan in the losing presidential campaign of 2012, and of a piece with then-President George W. Bush’s failed efforts to transform Social Security from a federally guaranteed pension system to something more akin to a private 401(k) plan.

Mr. Romney’s 2012 proposals were taken from the bipartisan commission assembled to address the budget deficit during Barack Obama’s presidency. The recommendations went nowhere.

Ms. Haley’s calls to stand by NATO and support Ukraine echo the foreign policies of every president since the Second World War, but particularly the Republicans, Ronald Reagan and George H.W. Bush.

But Mr. Trump has been relentless in his attacks on all those policies. His constant suggestions that he could withdraw the United States from NATO prompted President Biden last month to sign legislation barring the president from unilaterally dropping the North Atlantic alliance.

At a rally in Concord, N.H., Friday night, he portrayed Ms. Haley as someone who “wants to wipe out your Social Security,” raise the retirement age to 75, “and then you’re dead.”

A radio ad placed in New Hampshire on Friday said Ms. Haley’s “devious plan” would “shockingly change the rules” on federal programs for the older Americans by raising the retirement age. A television ad, titled “Threat From Within” and placed the day before featured retirees looking stricken as they hear that “Haley’s plan cuts Social Security benefits for 82 percent of Americans,” before being reassured, “Trump will never let that happen.”

The ads are false. The 82 percent figure stems from the total number of Americans eligible for Social Security, and Ms. Haley has said repeatedly that she would change nothing for current recipients or those close to eligibility.

Republicans are used to coming under fire for the types of ideas that Ms. Haley is pushing. But this time, it’s coming from the party’s de facto leader.

“Whenever you discuss Social Security in a rational way, you’ve immediately gotten skewered, usually by the left,” said Judd Gregg, a retired Republican senator from New Hampshire who made long-term deficit reduction his main cause in Congress. “But in this case it’s by Donald Trump.”

Mr. Trump and his Republican allies in Congress have been pushing their own form of fiscal discipline, couching ending aid to Ukraine and other domestic spending cuts as deficit reduction.

In truth, their target for cuts mathematically could never put a dent in the federal deficit, which is expected to swell to nearly $1.7 trillion in the fiscal year that ends this Sept. 30, up from $1.4 trillion in fiscal 2023.

About 85 percent of the federal budget goes to Social Security, Medicare, other entitlement programs like veterans benefits, the military and interest on the national debt — none of which are on Mr. Trump’s target list. That leaves just 15 percent of total spending, for education, law enforcement, transportation, medical and other scientific research, energy, national parks, and foreign assistance.

And with interest rates at their current high levels, even liberal economists worry that if Washington doesn’t start addressing the red ink, the rising cost of paying the government’s debts will crowd out other programs, stifle private investment and hurt the nation’s long-term future. Already, interest payments reached $659 billion last year, the fourth largest item in the federal budget.

“In 10 years, the government will be spending more on interest on the national debt than on defense,” warned Thomas Kahn, who was the Democrats’ staff director on the House Budget Committee for 20 years. “The reality is the national debt is out of control, and both parties will need to make politically painful decisions.”

Ms. Haley has not broached the ultimate painful decision for Republicans, raising taxes, but she has hit Mr. Trump repeatedly for adding $8 trillion to the federal debt while in office, after promising in the 2016 campaign that he would not only balance the budget but would pay off the debt, which surpassed $34 trillion over the holiday season.

Those attacks appear to have delivered only glancing blows to Mr. Trump’s dominance. The former president won the Iowa caucuses on Monday in a landslide, with Ms. Haley a distant third. Polls point to a narrower Trump victory in New Hampshire on Tuesday, then a steep uphill climb for Ms. Haley ahead of the South Carolina primary next month in her home state.

But like a modern-day Cassandra, Ms. Haley has not flinched from her warnings that the nation must act now to curtail spending rationally in the largest government programs, Social Security and Medicare, or face more painful, chaotic cuts in the future.

“I have seen the commercials you’ve seen,” she told voters on Wednesday in Rochester, N.H. “I will always tell you the truth.”

The truth is not pretty. The bipartisan trustees of Social Security say if nothing is done, the main Social Security program, the Old-Age and Survivors Insurance Trust Fund, will deplete its reserves in 2033, which could be the end of a Haley second term. At that point, Social Security would have to rely only on the money coming in from taxes each year. Promised benefits would have to be cut by 23 percent, not for future retirees that Ms. Haley wants to target but for those already drawing benefits.

“The only person who wants to cut Social Security is Trump,” said Nachama Soloveichik, the Haley campaign communications director. “Trump’s refusal to save Social Security means 100 percent of Americans will face a 23 percent cut in Social Security benefits in less than 10 years.”

Steven Cheung, a spokesman for the Trump campaign, dismissed such criticism as still more evidence of Mr. Trump’s righteousness.

“Nikki Haley is spiraling out of control and is now resorting to outright lies because she knows her position of increasing the age for Social Security and slashing retirements is an untenable position,” he said. “She should look deep down inside and really address why she wants to throw hard-working Americans off a financial cliff.”

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