LOS ANGELES (CBSLA.com/AP) — Hundreds marched through downtown Los Angeles protesting President Donald Trump’s plan to dismantle his predecessor’s signature health care law.

The demonstration Thursday came as congressional leaders postponed a vote on the American Health Care Act, which the White House hopes will replace Obamacare.

A marcher who identified herself as Ann said she works at a South LA healthcare clinic said their clients rely heavily on the Affordable Care Act.

“It’s very important that we keep it going strong, to keep providing services to the people who need it most,” she said.

Protesters cheered loudly when the postponement was announced.

Marchers hoisting signs reading “save our health care” said people have come to rely on coverage provided by the President Barack Obama’s plan. They said they fear millions of Americans would be left without health coverage.

The rally coincided with similar events across the state and nation.

GOP leaders hope to reschedule a vote Friday.

CBS2’s Amy Johnson spoke to many in the crowd who said they were willing to keep up the pressure on the GOP to keep their hands off their healthcare.

“I thought it was critical that we make a statement here in Los Angeles that we want to save Obamacare,” said Jim Mandia, CEO of St. John’s Well Child and Family Center.

He helped organize the rally- so people like Tawana Thomas could have a voice.

“I would support this every single day..I’ll be back tomorrow and the next day and the next day and the next day because I’m so worried about this I can’t sleep at night,” said Thomas.

The mother of four came from Lancaster- She told Johnson she suffers from seizures.

“I take three medications and I wouldn’t be able to afford my medicines,” she said.

And without her meds? “More seizures.”

“Now is the time for our nation to come together — and move in the right direction. To make sure we defend the progress we have made and that we move forward,” said LA City Councilman Gil Cedillo.

(© Copyright 2017 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)