She did not reference the Senate funding measure, but said she could support a bill that funded the government for up to 10 days.
She's still not a fan of the Affordable Care Act, but said it "would be impossible" to completely repeal the measure. At this point, Capito thinks the national debate is shifting.
"I think the Obamacare issue has probably taken the back seat now to the debt ceiling and what we're going to do," she said.
Many Republicans want any debt-ceiling solution to significantly reduce spending. Democrats have argued those reductions are too severe and new revenue - taxes, typically - should not be left off the table.
Like Boehner and McKinley, Capito believes there can't be any solution if the president won't negotiate.
Like the "clean" resolution to fund the government, Senate Democrats are considering introducing a measure that would raise the borrowing limit without any other policy measures attached, according to Bloomberg News.
Bloomberg also reports as many as seven Republicans could support the measure, enough to successfully pass the bill if every Democrat also votes in favor.
Manchin isn't sure how he'll vote, though. A spokesman said the senator would need to see any plan before he'd support it, but he is in favor of a "grand bargain" in the vein of a deficit reduction measure introduced earlier in the year.
The senator did take action on a shutdown issue drawing further national criticism.
The Department of Defense announced it could not provide death benefits to the families of soldiers killed while on active duty - $100,000 per family - because it lacked enough federal funding.
In a news release, Manchin said the private Fisher House Foundation agreed to cover the costs until it could be federally reimbursed.
Lawmakers agreed to try and approve federal funding for such costs as soon as today.