WASHINGTON — Representative Kevin McCarthy of California finally secured the House speakership in a dramatic vote ending around 12:30 a.m. Saturday, but the dysfunction in his party and the deal he struck to win over holdout Republicans also raised the risks of persistent political gridlock that could destabilize the American financial system.

Economists, Wall Street analysts and political observers are warning that the concessions he made to fiscal conservatives could make it very difficult for Mr. McCarthy to muster the votes to raise the debt limit — or even put such a measure to a vote. That could prevent Congress from doing the basic tasks of keeping the government open, paying the country’s bills and avoiding default on America’s trillions of dollars in debt.

The speakership battle that spanned more than four days and 15 rounds of votes suggested President Biden and Congress could be on track later this year for the most perilous debt-limit debate since 2011, when former President Barack Obama and a new Republican majority in the House nearly defaulted on the nation’s debt before cutting an 11th-hour deal.

“If everything we’re seeing is a symptom of a totally splintered House Republican conference that is going to be unable to come together with 218 votes on virtually any issue, it tells you that the odds of getting to the 11th hour or the last minute or whatever are very high,” Alec Phillips, the chief political economist for Goldman Sachs Research, said in an interview Friday.

The federal government spends far more money each year than it receives in revenues, producing a budget deficit that is projected to average in excess of $1 trillion a year for the next decade. Those deficits will add to a national debt that topped $31 trillion last year.