Republican members of Congress held a news conference Thursday urging the Senate to pass a measure to restore funding to the National Institute of Health. (The Washington Post)

A group of leading House Republicans donned lab coats this week and took to a Capitol Hill news conference to plead for passage of a bill that would restore funding for the National Institutes of Health amid the government shutdown.

“Whether it’s pediatric cancer research, diabetes, so many other cures and treatments that are being developed — we don’t want to put them on hold,” Rep. Cathy McMorris Rodgers (Wash.) said Thursday. “We want America to continue to be the leader.”

Yet three days earlier, McMorris Rodgers joined other Republicans in deciding to shut down NIH and other parts of the government after President Obama refused to curtail his health-care law.

McMorris Rodgers, who has a child with Down syndrome, “has always supported the critical medical research at NIH, especially because she has a personal connection to the difference it can make in the lives of millions of families and children with disabilities,” a spokesman said.

In ways big and small, Republicans and Democrats are trying — and often struggling — to square their strategy for overcoming the ongoing government shutdown with their prior positions.

See why some House Republicans might support a clean budget bill.

The challenge has been greatest for Republicans, who forced the partial government closure at midnight Monday by refusing to pass a funding bill unless Obama agreed to defund or delay the new health-care law. Many Republicans spent the remainder of the week bemoaning programs that had been closed and trying to restore funding to individual agencies through piecemeal legislation.

Democrats, meanwhile, have faced the challenge of standing unified against the GOP strategy, refusing to agree to open agencies that they generally support. Dozens of Democrats have broken ranks, however, voting with Republicans in favor of restoring funding for the District and for veterans programs.

The net effect is a sort of political cognitive dissonance: Republicans demand to reopen some agencies but not the whole government, while Democrats oppose relief unless everything is restored.

Rep. Randy Neugebauer (Tex.) illustrated the risks of the GOP approach this week when he publicly railed against a National Park Service ranger working at the National World War II Memorial on the Mall. The monument was closed when the government shut down.

In a moment captured on a widely viewed video, Neugebauer stood by a group of veterans and asked the female ranger, “How do you look at them and deny them access?”

The ranger responded, “It’s difficult.” Then the congressman said: “The Park Service should be ashamed of themselves.”

Veterans at the memorial started to defend the ranger by shouting at Neugebauer, “This woman is doing her job,” and telling him to do his.

The congressman’s Facebook page was later inundated with critical messages, including some from the veterans he was aiming to support.

A spokeswoman for Neugebauer did not respond to an e-mail seeking comment.

Other Republican lawmakers have faced criticism for accepting salaries while federal workers aren’t getting paychecks. Rep. Renee L. Ellmers (N.C.), who supported the shutdown, told radio station WTVD in Raleigh that she could not afford to give up her $174,000 salary.

The thing of it is, I need my paycheck. That is the bottom line,” Ellmers said.

She faced immediate criticism from her home state. “We appreciate the fact that Rep. Ellmers is living paycheck to paycheck, like so many hardworking North Carolinians, making it all the more unfortunate that she refuses to earn her paycheck and work toward a commonsense solution to end this self-inflicted crisis,” the state Democratic Party said in a statement.

On Friday, Ellmers announced she would give up her compensation while the shutdown lasts to “stand with all federal workers.”

On restoring funding to NIH, Republicans have made emotional pleas after news reports that children with cancer were being turned away from clinical trials. The GOP has passed a bill in the House to restore funding to NIH, but the Senate has refused to take it up as a one-off bill.

Wearing a lab coat at the Thursday news conference focused on NIH, Rep. Todd Rokita (R-Ind.) said, “Families, faith communities, associations and neighbors can take care of us better than government programs can.”

But he said there are areas where government is important, including NIH. He noted that his son has a rare neurological disorder that could benefit from NIH research.

“Without the help of programs that are at the NIH and other private-sector programs, we may never know,” he said.

Some public health experts said it makes little sense to simply restore funding to specific programs.

“The NIH isn’t the only research institution in the government,” said Georges C. Benjamin, the executive director of the American Public Health Association. “There are many, many, many other health agencies that provide health services that are just as critical and just as important.”

Democrats have gone along with a few carve-outs to the shutdown, most notably agreeing to pay military salaries. But for the most part, they have refused to entertain bills to open war memorials, fund NIH, fund the veterans department and take other steps to reopen specific federal functions.

The unified strategy has opened Democrats to criticism that they are brushing off the chance to lessen the closure’s negative effects.

Del. Eleanor Holmes Norton (D-D.C.) gave an impassioned speech in the House imploring her colleagues to restore funding for the District. And Sen. Bernard Sanders (Vt.), an independent who caucuses with Democrats, has argued in favor of a bill funding veterans programs.

But other Democrats say they must stand unified against what they have called GOP “gimmicks.”

“What right do they have to pick and choose what part of government’s going to be funded? It’s obvious what’s going on here,” Senate Majority Leader Harry M. Reid (D-Nev.) said this week.