Washington — The Senate on Thursday rejected a pair of bills to address rising health care costs, with lawmakers unable to reach a bipartisan agreement on extending tax credits that help millions of Americans purchase insurance under the Affordable Care Act.

But with the partisan exercise behind them, some senators are expressing tepid optimism about a path forward on a compromise. Lawmakers who had sought a bipartisan path forward in recent weeks have said the failed votes could be key to unlocking a deal that would extend the subsidies with reforms aimed at addressing fraud. Four Republican senators joined Democrats in voting to extend the subsidies on Thursday, hinting that an agreement might be possible.

"After we fail, I like to think we succeed," Sen. Lisa Murkowski, an Alaska

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