The Post's Capitol Hill reporter Ed O'Keefe discusses the week to come on Capitol Hill as the shutdown continues, and the debt ceiling deadline nears. (The Washington Post)

One week into the first federal government shutdown since 1996, the Republican Party remains hostage to an unrealistic strategy aimed at an unattainable goal — defunding the nation’s health-care law — that had no obvious path to success.

The shutdown is disruptive and uneven, causing some pain and wider unease if only because of its unpredictability. It also is less encompassing today than it was when it began. House GOP leaders have simultaneously attempted to maintain unity while trying to escape possible political blame for the consequences of what their strategy could lead to.

At this point, no one looks particularly good to the public, but congressional Republicans are faring worse than Democrats and much worse than President Obama.

A new Washington Post-ABC News poll shows that 70 percent of Americans disapprove of the way Republican lawmakers are dealing with the budget negotiations, seven points higher than a week ago. Only half of all Republicans approve of what their congressional wing is doing.

Democrats in Congress look worse in the latest survey as well, with 61 percent of Americans saying they disapprove of them, five points higher than last week. Obama’s rating rose slightly, with 51 percent disapproving and 45 percent approving.

The struggle has exposed a rift between the party’s confrontational, populist, tea party wing and its traditional business and establishment wing. These tensions reflect fundamental questions about the direction of a party whose rightward shift over the past decade has helped intensify the political conflict and changed the calculus of governance generally.

The conservative movement is not deeply divided over philosophy and policy. Obamacare is unpopular across the spectrum of conservatism, and the president is distrusted by many conservatives who do not consider themselves tea party followers. Overall, virtually all elements of the Republican coalition are more conservative and more hostile to the government than they were in the past.

But Republicans are divided about whether to be a party of “no” or a party that can fashion a more positive vision for conservative governance. The shutdown has brought these differences into even sharper focus. But if there is an obvious resolution, party leaders haven’t found it.

Tea party activists view compromise as capitulation to policies destroying the country and to a president they despise. Mainstream conservatives don’t particularly trust the president either, and oppose much of his agenda. But they question the tactics of the tea party wing, particularly in the shutdown battle. They recognize the inherent risks of being defined by their most hard-line faction. The unease of many Republican governors and other conservatives about the course the House pursued reflects this tension.

However, the perceived power of the tea party — and of those who help fund its members and threaten primary challenges to those who do not hew to the line — continues to make more traditional conservatives wary of staking out positions that are overtly critical of those forces.

The way the shutdown has played out reflects these tensions. Even before it officially began, Republican leaders were looking for ways to shield themselves from any political fallout. In the process they have found themselves defending many parts of government after long denigrating much of it.

Their first effort was to push legislation assuring that active-duty military members would continue to be paid through the shutdown. No one wanted to be on the wrong side of that vote. Obama and the Democrats quickly agreed to go along with that. Emboldened, Republicans decided to try to raise the pressure on the Democrats. Instead they dug themselves deeper.

With the shutdown underway, they tried to rewrite the normal congressional appropriations process (which is in a shambles right now) by offering a series of bills that would selectively fund popular programs and personnel. They wanted to help veterans and the National Institutes of Health. The message they have conveyed is that, until they get concessions on the health-care law, they will keep the government closed except for the parts they want to be open. This time, Obama and the Democrats refused to go along.

Meanwhile, Republicans expressed surprise and outrage that government monuments or park areas controlled by the National Park Service have been closed or restricted, claiming the president was being punitive and political. Some House Republicans went to the World War II Memorial and barked at Park Service employees to show their displeasure.

The shutdown is becoming a checkerboard of things functioning and things closed. Significant portions of the government were never to be shut down. Mandatory spending programs were exempt from the beginning. Social Security checks have continued to go out.

Over the weekend, Defense Secretary Chuck Hagel called back almost all civilian employees of his department. At the same time, the House passed another bill assuring that all furloughed federal workers will receive back pay when the shutdown ends. The vote was unanimous.

Even some House Republicans question the logic of continuing the shutdown under these circumstances, but logic has not been the prevailing motivator these past two weeks.

Given the mandatory carve-outs and the decision to guarantee back pay for all workers, the shutdown will not save money. But it continues to leave programs and people who depend on the government for help, but who have little clout or visibility, vulnerable until everything officially reopens.

On Sunday, House Speaker John A. Boehner (R-Ohio) remained defiant during an appearance on ABC’s “This Week.” He said there were not enough votes in the House to pass a “clean” bill to reopen the government, even on a short-term basis. Democrats and some Republicans dispute Boehner’s claim that a spending measure shorn of demands by his party to somehow change the health-care law could pass the House. On Monday, Obama dared him to put the legislation on the floor.

With hopes of blocking Obamacare in Congress nonexistent, Boehner appeared Sunday to shift his focus to the Oct. 17 deadline for raising the federal debt ceiling. He drew another bright line. “The votes are not in the House to pass a clean debt limit,” he said. Boehner demanded that Obama begin negotiating with Republicans. “He knows what my phone number is,” the speaker said of the president. “All he has to do is call.”

The dangers for Boehner and the Republicans are obvious. The longer this standoff continues, the more he and his leadership team will be defined by the most hard-line constituency in the GOP coalition. Obama has his own calculations to make as the debt-ceiling deadline nears and he weighs the consequences of default and whether there is any realistic prospect for a deal on entitlements, spending and taxes. But it is the Republicans who decided to risk pushing the country to the brink.