WASHINGTON — Republicans have pledged to “repeal and replace” President Barack Obama’s health-care overhaul. If the Supreme Court strikes down the law, they may struggle to deliver on the second part of their vow.

A plurality of Americans, 43 percent, say they want to retain the 2010 law with only small modifications, while 15 percent say the measure should be left alone, a Bloomberg National Poll shows. One-third say it should be repealed.

The court will rule in the next week on the constitutionality of the law, the centerpiece of which is the mandate that most Americans buy insurance or pay a fine.

A rejection of all or part of the Affordable Care Act would be a setback for Obama, undercutting his biggest legislative victory. It would also present a challenge to Republicans. With elections approaching, House Republicans are signaling they have no immediate replacement to offer.

“If you’re out to get more votes in six months, coming forward with a detailed program is not the optimal strategy,” said Henry Aaron, a health-policy scholar at the Brookings Institution in Washington. Republicans have little to gain in proposing a comprehensive plan since it may draw criticism from health-care providers or consumers, he said.

House Speaker John Boehner, R-Ohio, said on Tuesday that the House would take a “step-by-step approach” to revamping health care.

A number of the law’s features are popular. Laetitia Adam, a 33-year-old independent voter from Miami, said she supports the insurance mandate as well as the provision allowing children up to age 26 to stay on their parents’ health plans.

“For the most part, I agree with the law as it is,” Adam, a respondent to the June 15-18 poll, said in a follow-up interview. “You can’t afford to get sick without insurance,” said the graphic artist. The law just “needs to be made more simple.”

In a nod to public support for aspects of the law, insurers UnitedHealth Group, Aetna and Humana said this month they would retain some benefits even if the court strikes down the law, including allowing young adults to stay on their parents’ plans and offering free preventive care.

The partisan divide over the health-care plan was underscored in 2010, when the legislation passed a then- Democratic-controlled Congress with no Republican votes.

Republican leaders now are mapping out a legislative response to a possible Supreme Court rejection of that law, which is intended to expand coverage to at least 30 million uninsured Americans.