WASHINGTON — Senator Claire McCaskill, Democrat of Missouri, was the first to take to the Senate floor to publicly pose a question gnawing at an increasing number of lawmakers and ordinary citizens alike as the deadline for a government shutdown neared: Has Congress gone completely crazy?

“It’s very hard from a distance to figure out who has lost their minds,” said Ms. McCaskill immediately after the Senate on Monday rejected a Republican plan to not finance the government unless Democrats agreed to delay the new health law. “One party, the other party, all of us, the president.”

Senator Harry Reid, the Nevada Democrat and majority leader, had his own colorful, if somewhat skewed, metaphor about why much of the government was about to grind to halt in a take-no-political-prisoners fight over what is essentially a simple six-week funding bill, attributing it to the emergence of a “banana Republican mind-set.”

Mr. Reid’s language was evocative, and the implication was serious. With Democrats controlling the White House and Senate and with millions of dollars spent getting the health care law to the starting line, what gives House Republicans the idea that they can triumph in their push to repeal, or at least delay, the Affordable Care Act when so many veteran voices in their party see it as an unwinnable fight?