Abortion rights supporters slammed the bill, with Diana Gómez, advocacy manager at Progress Texas, asserting that "this abortion ban contains some of the most extreme abortion restrictions in the country."

"Let me be clear: Abortion is health care and it is still legal in Texas," she said in a statement. "This six-week abortion ban is unconstitutional and others like it have been struck down by federal courts across the nation. Roe v. Wade is still the law of the land and regardless of whatever bill Gov. Abbott signs, no law will stop abortions from happening."

Among the increasingly common heartbeat bans passed this year, however, Texas' bill is unique in that it includes a provision opening anyone who aided in accessing such an abortion to legal liability.

It allows for civil charges to be brought against those who provide abortions after the detection of fetal heartbeats, as well as anyone who "knowingly engages in conduct that aids or abets the performance or inducement of an abortion, including paying for or reimbursing the costs of an abortion through insurance or otherwise," after the onset of a fetal heartbeat. Those found guilty would face a $10,000 fine for each abortion performed or facilitated.

Multiple Texas House Democrats decried the measure going into the vote. When Slawson said that people who successfully bring claims against those who provide or facilitate abortions in violation of the heartbeat ban would receive the $10,000 sum dictated by the bill, Democratic state Rep. Nicole Collier said that "it's just like a lottery, basically."

"There will always be women who will pursue having abortions despite what you do here today and what you've been doing for a decade to create all these obstructions," said state Democratic Rep. Donna Howard, a former nurse. "It will always be a case that women will seek abortions, because women are not always in a position to have that baby. And you guys don't have to have them, we do. It affects our lives."

Texas state Sen. Bryan Hughes, the bill's sponsor in the Senate, told CNN before the bill's signing that "it was time for Texas to pass a heartbeat bill. We looked at what other states had done, looked at what the Supreme Court and other federal courts have said about abortion and what states can do, and took all that into account to come up with Senate Bill 8."

Regarding the lack of exceptions for rape and incest victims, Hughes said, "Let's do everything we can to hold people accountable who do something like that, to protect women from that," adding, "Let's harshly punish the rapist, but we don't, we don't punish the unborn child."

That same provision, he believes, could get the bill farther along in an anticipated court challenge, based on signs from higher courts that have considered similar restrictions.

"Based on what we read in court opinions from other abortion cases, and other federal cases, we believe this bill -- because of the private civil enforcement, primarily, and a few other things -- is drafted differently than those other heartbeat bills that are pending, that are awaiting court ruling today," he said.

Leaders of Texas abortion funds -- which help pay for the procedure and related expenses for abortion seekers who cannot afford them -- have decried the bill as putting their organizations, as well as abortion seekers' friends, in legal jeopardy.

The bill "allows literally anyone, including non-Texas residents who maybe have zero connection to the person having an abortion, it allows them to use lawsuits to harass people who help people access abortion care after six weeks," Amanda Williams, executive director of the Lilith Fund, told CNN. "That would also obviously include us, as an abortion fund, who helps people access abortion care."

"These are expensive. This is our time and our resources," she said of hypothetical challenges against the group, which she noted does not have a legal budget. "If we were to be hit by frivolous lawsuits left and right, I mean, this would really prevent us from doing our work in a lot of ways."

This story has been updated with additional information.