Democrats and Republicans are each saying they still want to improve the health-care system in the wake of the GOP’s failed effort to repeal and replace Obamacare, but a piece-by-piece strategy appears much more likely than a sweeping reform.

Stefanie Miller of Height Securities said prospects for Senate Majority Leader Mitch McConnell trying to revive a repeal of the Affordable Care Act are “highly unlikely,” and told MarketWatch she believes the most that the two parties will be able to agree on is extending “cost-sharing reduction” payments.

President Donald Trump has threatened to cut off those payments, which reimburse insurers for lowering deductibles and copayments for millions of people who get insurance under Obamacare. But Miller believes it’s likely Congress will commit to a long-term fix for the payments. She says uncertainty about the payments from month to month is what has led some insurers to pull out of Obamacare exchanges, and Congress locking in funding by mid-September would let insurers price plans for 2018.

Even if Republicans give up on outright repeal of Obamacare, they could still chip away at parts of it. One potential target is repealing the 2.3% medical device tax, currently set to be reinstated on Jan. 1. It was suspended by Congress for 2016 and 2017 after taking effect in 2013. But it is a perennial source of criticism and has foes from both parties — Sens. Al Franken and Amy Klobuchar of Minnesota are two Democrats who have called for its repeal. Device maker Medtronic’s MDT, -0.46%   operational headquarters are in Minnesota.

Another target, says Miller, is Obamacare’s health insurance tax, or HIT. The insurance industry argues the tax “directly increases the premiums that people pay,” and has pushed for it to be repealed. There is currently a moratorium on the tax and Miller, citing strong industry lobbying, says she thinks it and the device tax will both be delayed again. The HIT also goes back into effect in January, absent congressional action.

In the wake of the failure of the “skinny” repeal bill early Friday morning, McConnell said he wanted to hear Democrats’ plans.

“I think it’s appropriate to ask, ‘what are their ideas?’” the Kentucky Republican said. But he also laid down a marker by saying that “bailing out insurance companies with no thought of any kind of reform is not something I want to be part of.”

His Democratic counterpart, Chuck Schumer of New York, said “let’s turn the page and work together to improve our health-care system.”

At a news conference on Friday, Schumer said “at the very beginning, we should stabilize the system” by making the cost-sharing payments permanent.

He also said the Senate should consider a reinsurance program for the individual health market — and noted that Republican Sen. Susan Collins of Maine has a such a bill with Democrat Bill Nelson of Florida. Nelson told reporters last week that he was “working with” Collins. “In the case of the insurance company that has a catastrophic loss, you create a reinsurance fund,” Nelson said. “You insure the insurance company against the catastrophe.”

At the very least, both sides are committed to holding more hearings about health care. Senate Health Committee Chairman Lamar Alexander, a Tennessee Republican, said more than a week ago that he would hold hearings on stabilizing the individual health-insurance market. Speaking to CNBC on Friday morning, House Democratic Whip Steny Hoyer of Maryland said “I think the committees will work hopefully in a bipartisan fashion [and] have hearings” to improve Obamacare