Markets have grown concerned about the rapid pace of borrowing and spending by the federal government, but if Trump successfully addresses the US debt problem, stocks could be on the verge of an "everything rally," market veteran Ed Yardeni said on Monday.

Optimism that Trump may help the government exercise more fiscal constraint is brewing in the bond market, the Yardeni Research president said, pointing to the rally in bonds following Trump's recent election win.

That could be a sign that some of Trump's proposed policies have appeased bond market vigilantes , he added, referring to investors who could protest government borrowing by staging a sell-off in Treasurys.

"I think that the Trump administration — incoming administration — bought some time, kind of placating the bond vigilantes by basically acknowledging that we got a problem with the deficit," Yardeni said, speaking to CNBC on Friday.

Yardeni added that markets could be verging on a "Bill Clinton moment," referring to the conservative fiscal policy Clinton implemented during his years in office. That restraint resulted in the a US budget surplus and an impressive run-up in stocks.

"It becomes an everything rally. The only risk is that it becomes too much of a good thing. It becomes a meltup, and we're kind of on the edge there," Yardeni said, referring to his idea that there could be an unsustainable stock boom .

It's unclear how Trump's second term will shape the US debt picture. Economists have said some of Trump's proposed policies — like his plans to cut taxes and deport undocumented immigrants — could end up adding trillions to the national deficit and debt .

But other proposed policies — like his plans to levy tariffs on US imports — could boost federal revenues, narrowing the budget deficit.

Investors may also be feeling more optimistic about the US debt picture due to proposed government spending cuts , put forth by the new Department of Government Efficiency, as well as Trump's Treasury Secretary pick, Scott Bessent, a former Wall Street exec who said that one of his top priorities will be shrinking the US debt.

Broadly, Yardeni sees a strong backdrop for stocks into 2025 , predicting the US will continue to avoid a recession and that the rally in stocks will continue to broaden. Signs of a wider market rally are already beginning to emerge, he said, pointing to recent strength in small- and mid-cap stocks .