Joe Biden and top Democrats are scrambling for a strategy to counter Republican restrictions on women’s reproductive rights amid the fallout from a Texas statute that has banned abortions in the state from as early as six weeks into pregnancy – but the options available to the administration are thin.

The conservative-dominated supreme court in a night-time ruling refused an emergency request to block the Texas law from taking effect, in a decision that amounted to a crushing defeat for reproductive rights and threatened major ramifications in other states nationwide.

Even as the US president on Thursday accused the court of carrying out an assault on vital constitutional rights and ordered the federal government to ensure women in Texas retained access to abortions, the future of reproductive rights remains in the balance.

The challenges facing Biden and Democrats reflect the deep polarization of Congress, and the difficulty in trying to force bipartisan consensus on perhaps the most controversial of issues in American politics.

Now, top Democrats in Congress have developed a multi-part strategy to roll back restrictions pushed by Republican-led states that rests on attempting to codify abortion rights protections into federal law – and potentially to reform the supreme court.

The House speaker, Nancy Pelosi, announced on Thursday that Democrats would vote within weeks to pass the Women’s Health Protection Act, a bill that would ensure the right to access an abortion and for medical providers to perform abortions.

“Upon our return, the House will bring up congresswoman Judy Chu’s Women’s Health Protection Act to enshrine into law reproductive healthcare for all women across America,” Pelosi said in a statement that also admonished the court’s decision.

Separately, liberal Democrats led by progressives including the New York congresswoman Alexandria Ocasio-Cortez are urging Biden to strike down other restrictions on access to abortions and the Hyde amendment, a measure that prohibits federal funding for most abortions.

Seizing on the Texas decision, liberal Democrats have also called anew for an expansion of the supreme court from nine to 13 seats, which would enable Biden to appoint four liberal-leaning justices to shift the politics on the bench.

The legislative response is aimed at reversing more than 500 restrictions introduced by Republican state legislatures in recent months and “trigger laws” that would automatically outlaw abortions if the supreme court overturned its ruling in the landmark Roe v Wade case that was supposed to cement abortion rights in the US.

But while such protections are almost certain to be straightforwardly approved by the Democratic-controlled House, all of the proposals face a steep uphill climb in the face of sustained Republican opposition and a filibuster in the 50-50 Senate.

The Senate filibuster rule – a procedural tactic that requires a supermajority to pass most bills – was in part why the Senate Republican leader, Mitch McConnell, focused on stacking the supreme court with conservative justices rather than pursue legislation to enact abortion restrictions at a federal level.

Forty-eight Democrats currently sponsor the Women’s Health Protection Act in the Senate. Two Republicans – Senators Susan Collins and Lisa Murkowski – have previously indicated support for abortion rights, but the numbers fall far short of the 60-vote threshold required to avoid a filibuster.

Against that backdrop, a majority of Senate Democrats have called for eliminating the filibuster entirely. But reforming the filibuster requires the support of all Democrats in the Senate, and conservative Democratic senators including West Virginia’s Joe Manchin and Arizona’s Kyrsten Sinema are outspoken supporters of the rule.

The broad concern demonstrates how urgent the issue has become for Democrats, and with the Texas law in effect after the failure of the emergency stay, many reproductive rights advocates worry that Democrats will be unable to meet the moment with meaningful action.