Wendy Davis speaks about a recent Supreme Court ruling on easing HB2, a Texas state abortion law, on October 16, 2014 in Houston, Texas.
CNN  — 

Supporters of abortion rights filed a new federal lawsuit Tuesday in the latest bid to prevent enforcement of Texas’ six-week abortion ban, which has dramatically reduced access to the procedure in the country’s second largest state.

Critics of the Texas law suffered a huge loss in December, when the US Supreme Court allowed the novel law – written with the intent to make it almost impossible to challenge – to remain in effect.

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In Tuesday’s lawsuit, an abortion fund that helps Texas residents pay for the cost of abortion care and three donors, including former Democratic state Sen. Wendy Davis, are seeking to sue private individuals who have promised to try to enforce the controversial law against the funds, their donors, employees and volunteers.

In court papers they call the law “blatantly unconstitutional” and say it “incentivizes vigilante harassment of anyone who assists abortion patients.”

Under the law, state officials are generally barred from enforcing the statute. Instead, individuals from anywhere in the country can file suit against someone they think might be helping a woman obtain the procedure. They can also collect damages of more than $10,000. The threat of such lawsuits has discouraged doctors from performing abortions after six weeks. Since the decision, other states have moved to pass similar laws.

The lawsuit comes as states hostile to abortion rights are moving aggressively to pass harsher restrictions. In addition, the Supreme Court is currently considering a request from Mississippi to overturn Roe v. Wade in the most important abortion-related case the justices have heard in some 30 years.

If Roe were overturned or fundamentally weakened, 21 states have laws or constitutional amendments already in place to attempt to ban abortion as quickly as possible, according to the Guttmacher Institute, which favors abortion rights. An additional five states are likely to ban abortion as soon as possible without federal protections. As of this month, 536 abortion restrictions have been introduced in 42 states.

The abortion fund behind the suit is called the Stigma Relief Fund. It is represented in court by Stephanie Toti of The Lawyering Project. In court papers, Toti is asking the court to hold that the law is unconstitutional and “unenforceable.”

In court papers, Toti says the law has had an “immediate and devastating impact” on all Texans, “which is felt most acutely by the marginalized communities that abortion funds serve.”

The fund is suing Texan resident Mistie Sharp, who has sworn in court that she intends to sue abortion funds, as well as Sadie Weldon and Ashley Maxwell “because they have taken aggressive steps to sue certain Texas abortion funds and their donors, employees, and volunteers.”

Even if the fund prevails in the lawsuit, however, it may not stop other individuals from attempting to enforce the law.