President Trump promised Wednesday that Republicans will take another stab at overhauling the U.S. healthcare system, an effort that collapsed when Senate GOP leaders failed to attract the support they needed to repeal and replace Obamacare.

During an event in Bismarck, N.D. that was meant to be a pitch for tax reform, Trump told the crowd that congressional Republicans are still working to tackle healthcare and may soon try a different approach.

"Believe me, we haven't given up on healthcare. We never give up," the president said, recalling the narrow 49-51 vote that sunk a Senate GOP measure to repeal President Obama's signature healthcare law in late July.

"One vote, think of it. One vote," Trump said. "Terrible, terrible situation that took place that night."

He continued, "We cannot let that happen again. But we'll get it done one way or another."

White House officials have continued to weigh various legislative options on healthcare reform that could appeal to both Republicans and Democrats, including an amendment proposed by Sens. Lindsey Graham, R-S.C., and Bill Cassidy, R-La., that would redirect federal spending on Obamacare to the states.

"[Trump] is ready with pen-in-hand to sign healthcare reform if, say, Graham-Cassidy moves forward," White House counselor Kellyanne Conway told Fox News on Wednesday. "People have been working on that very strongly over recess."

There is no telling when Republican leaders, who are currently focused on crafting a tax reform package that is capable of garnering bipartisan support, might shift their attention back to healthcare.

Trump has not offered a timeline for when he expects congressional healthcare negotiations to resume, though Conway said Wednesday that changes to the current system "should get done this year."