WASHINGTON — With Republican leaders pressing to dismantle the Affordable Care Act, possibly within weeks, moderate Senate Democrats reached out on Thursday to Republicans, appealing for them to slow down the repeal efforts and let lawmakers try to find acceptable, bipartisan changes to make the existing law work better.

Democrats also had new reason to hope for possible Republican defections after Speaker Paul D. Ryan of Wisconsin said that the repeal measure would cut off federal funds for Planned Parenthood. But for now, Republican leaders are holding firm. Senator Mitch McConnell of Kentucky, the majority leader, denounced the law, President Obama’s signature domestic achievement, as “a lesson to future generations about how not to legislate.”

Well before Republicans seized control of Washington, moderate Democrats and Republicans in the Senate had begun exploring ways to change the law, tempering its impacts on small business, seeking lower-cost insurance options and changing how quickly subsidies to help purchase insurance policies would phase out with rising incomes.

But those efforts were stymied by Republican leaders who had no interest in improving the health law and by Democratic leaders who saw reopening the law as a political Pandora’s box. Now, Democrats have every interest in opening that box as repeal efforts barrel forward, and they would need to peel off only a few Senate Republicans to slow the fast-track repeal movement.