WASHINGTON — As the administration struggles to put in place the final, complex piece of President Obama’s signature health care law, an endeavor on a scale not seen since Medicare’s creation nearly a half-century ago, Democrats are worried that major snags will be exploited by Republicans in next year’s midterm elections.

Many Democrats also want to see a more aggressive and visible president to push the law across the country. This week Mr. Obama is returning to the fray to an extent unseen since he signed the law in 2010, including a White House event on Friday to promote the law’s benefits for women, the first in a series of appearances for health care this year.

A number of health insurance changes have already taken place, but this fall, just as the 2014 election season heats up, is the deadline for introducing the law’s core feature: the insurance marketplaces, known as exchanges, where millions of uninsured Americans can buy coverage, with subsidies for many.

For the third time, Republicans are trying to make the law perhaps the biggest issue of the elections, and are preparing to exploit every problem that arises. After many unsuccessful efforts to repeal the law, the Republican-led House plans another vote soon. And Republican governors or legislatures in many states are balking at participating, leaving Washington responsible for the marketplaces.