New York City Mayor Bill de Blasio warned Wednesday that the Senate proposal to repeal and replace parts of the Affordable Care Act is “not dead” and said local leaders opposed to the legislation will continue lobbying lawmakers to vote against it.

“This bill is not dead by any stretch of the imagination,” de Blasio, a Democrat, told reporters on a conference call organized by the U.S. Conference of Mayors. “We saw a trajectory with the House bill that is cautionary. The first time around, it didn’t work, the second time around, it didn’t work, the third time, it did. We have to remember that the Senate bill is going to be looked at again over these next weeks.”

“That being said, I would say this time the difference is the Senate is a very different body, and not only are mayors, but lots of other voices of conscience around the country are really reaching out intensely and letting our senators know what a big impact it would make to lose this health care for so many of our people,” he continued. “I think the trajectory is different, but the ballgame is far from over.”

Local leaders, including some Republicans, have been some of the more vocal opponents of the GOP health care plan, which Senate Majority Leader Mitch McConnell had intended to bring up for a vote later this week.

The vote was delayed until after the Senate’s July 4 recess after several moderate and conservative Republicans announced their opposition to the proposal. McConnell can only afford to lose two votes from his conference for a bill to pass.

In addition to de Blasio, a group of mayors opposed to the bill largely hailing from Medicaid expansion states and those with moderate Republican senators spoke on the call on Wednesday. They described it as part of their plan to pressure lawmakers to drop their plans to repeal Obamacare on a party-line vote and come up with bipartisan fixes to the law instead.

The Republican mayor of Mesa, Arizona, John Giles, led off the call, and the mayors of Dayton, Ohio; Bangor, Maine; Reno, Nevada; Huntington, West Virginia; and Anchorage, Alaska spoke as well. Boston Mayor Marty Walsh provided a statement.

The mayors urged senators to reject the most recent draft of the bill, which they criticized for its cuts to Medicaid, lack of funding to address mental health and the opioid crisis, and potential impact on local hospitals.

“We can all agree that Obamacare is flawed,” Giles said. “We agree on that. But I need to point out that you don’t fix something by making it worse.”