Rep. Joe Kennedy Joseph (Joe) Patrick KennedyDemocrats see fundraising spike following Ginsburg death Massachusetts town clerk resigns after delays to primary vote count Bogeymen of the far left deserve a place in any Biden administration MORE III (D-Mass.) says he “would hope” to be able to support a revised "Medicare for all" bill next year, but said he has concerns with the current version of the bill.

Adding Kennedy as a co-sponsor of the Medicare for all bill would be a major boost in momentum for the effort, bringing on board a rising Democratic star whose legendary family has long been a leader in the push for universal health care.

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Kennedy has come under pressure from progressive activists to support the current version of the Medicare for all bill, known as H.R. 676. But Kennedy told The Hill that his concerns with the way the current bill is written prevent him from signing on.

Rep. Pramila Jayapal Pramila JayapalHillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Bipartisan representatives demand answers on expired surveillance programs DHS opens probe into allegations at Georgia ICE facility MORE (D-Wash.) is working on a revised version of the bill to introduce in the new session of Congress in January.

“I would hope I would be able to support that,” Kennedy said of the revised measure.

He says his concerns about the current bill include that it includes restrictions on abortion funding and could negatively affect investor-owned hospitals, which include Catholic hospitals in Massachusetts.

More broadly, he says the bill needs more vetting and detail, including spelling out how it would be paid for, and how its system of payment to doctors and hospitals would work.

The comments are a note of caution to progressives, who are energized at the prospect of voting on a Medicare for all bill now that Democrats have won back the House.

Kennedy said he “absolutely” supports the idea of single-payer health insurance, which has the government provide health insurance for everyone.

But he pointed to Republicans’ failure to repeal ObamaCare last year as a warning.

“I think that we have also seen over the course of the past two years that the details around health care actually matter,” Kennedy said.

“What I think needs to happen, which our Republican colleagues certainly did not do, to their detriment, is to actually come up with and put an awful lot of thought into what a strong single-payer bill would look like, and some of the alternatives, and actually flesh them out to get vetted,” he added.

Republicans have attacked the need for tax increases to pay for the trillions of dollars in costs of a Medicare for all, single-payer system.

“I think everybody's clear that taxes are going to have to go up in order to finance this,” Kennedy said, adding that the details of who gets taxed more matter. “How does that impact lower income families? How does it impact middle class families?” he said.

House Democrats are divided between progressives pushing for a vote on Medicare for all and more centrist members who want to take smaller, more measured steps to strengthen the Affordable Care Act.

Kennedy said he thinks “both” of those steps need to happen.

“There's no doubt that our country needs to continue this progress towards making sure that everybody gets access to health care that you need, when you need it, at a price you can afford,” he said. “That has been something that's one of the big driving motivators for me in my work here, it's been something that obviously members of my family have been working on for a very long time.”