As the end of the legislative session nears, Congress still has a considerable amount of work left to do and the outcome of that unfinished business will determine whether President Bush has much to show for his efforts this year.

Click in the video box to the right to watch a report by FOX News' Major Garrett.

Bush's polls are rebounding but the real test of his political clout will come this week as the GOP-led Congress tries to complete several bills in which Bush initiatives hang in the balance.

"I think it's a big challenge. He's facing some huge questions. Republicans on Capitol Hill are not unified, and that's something that he did enjoy in the past, he doesn't have now," said former Clinton Chief of Staff Leon Panetta.

The president has three big goals for Congress to achieve this week: Open the Arctic National Wildlife Refuge to oil and gas drilling, reduce future federal spending to offset the costs of Hurricane Katrina relief and extend the Patriot Act.

Top administration officials pressed Monday for drilling in ANWR.

"If we cannot do this in a state where the congressional delegation, the governor and the people strongly support energy development, then where in this nation will future generations of Americans look for their energy supplies?" asked Interior Secretary Gale Norton.

"Opening up ANWR is going to create new jobs and labor unions that support opening up ANWR have estimated that about 200,000 to 700,000 new jobs would be created," added Labor Secretary Elaine Chao.

Senate Republicans say they want ANWR drilling as part of an unrelated deficit reduction bill. Moderate House Republicans refuse. The president may have to choose one over the other.

Republicans are also tied in knots over extending the Patriot Act, which the president calls a crucial tool in penetrating terror networks. Three Senate Republicans are prepared to join a Democratic filibuster to stymie the bill.

The president has also pushed Congress to save money in spending in order to pay for Hurricane Katrina assistance while at the same time making his tax cuts permanent. On Sunday, Senate Majority Leader Bill Frist said he's hopeful spending and tax bills will get wrapped up soon, even if not all the work is done by year's end.

"I'm hopeful before we leave that we'll pass that spending reduction, cutting that growth and spending reduction reconciliation package, this week. I hope that the tax packages — both the House and the Senate will go to conference and possibly get it done before we go, but in all likelihood it will be soon after we get back in late January or February," Frist told FOX News Sunday.

Despite these problems, analysts predict the president, lifted by a series of Iraq speeches and a surging economy, will finish the year with a flourish.

"He's going to get a reconciliation bill that cuts spending, it saves some money. I think that's going to happen. He's going to get a compromise on the Patriot Act, re-authorizing that critical anti-terrorist piece of legislation. I think that it's ending up a better year than it started," said Vin Weber, a former Republican congressman from Minnesota.

The failure of the president's Social Security reform push earlier this year has led some to label him a lame duck. Republican decisions this week will either reinforce or reverse that perception.

"If they think sticking with the president will ensure their survival, then they'll be loyal. But if for one minute they think the president is not popular and is a hindrance with regard to their election back home, then they're going to basically be very independent and move out on their own," said Panetta.

Even with some victories, the president faces one unavoidable defeat — House passage of an immigration bill that ignores his call for a guest worker program.