House Republican leaders were forced to drop a proposal to open oil drilling in an Alaskan wilderness area to pick up needed votes to pass a deficit-reduction package.

But while Republicans compromised their drilling measure in the Arctic National Wildlife Refuge to appease party moderates on Thursday, no guarantee exists that the now-$51 billion deficit-reduction package will pass, sources told FOX News.

GOP leaders also agreed to drop a measure that would end a moratorium on offshore drilling on the continental shelf off the Atlantic and Pacific coasts.

Early Thursday afternoon, House leaders postponed debate until next week as more GOP lawmakers wavered in support.

House Democratic leader Nancy Pelosi said Republicans "simply do not have the votes."

"The Republican budget was about increasing the deficit, cutting taxes for the wealthiest Americans at the expense of the middle class and hurting those who need our help most -- hurricane survivors, seniors, students, and rural Americans," Pelosi said. "Democrats were united and made those issues too hot to handle for Republicans."

Despite setbacks to Republicans, the ANWR measure could still be brought back up in the final version to be negotiated in a House-Senate conference. The Senate has passed a drilling measure in its budget bill.

Some lawmakers who supported the ANWR provision had threatened to vote against the deficit bill if the drilling measure were scrapped. Those lawmakers were steered to the conference committee to try to resurrect the ANWR bill.

Republicans needed the votes of about 15 northeastern GOP moderates who had long opposed the drilling measure. GOP leaders decided to compromise once they realized they couldn't pass the deficit bill without the support of moderates, sources told FOX News.

Last time the House passed ANWR drilling, it had the support of some Democrats, but because the measure is attached to deficit reduction and Democrats are unified against cutting spending, Republicans had to keep their caucus together in order to pass the legislation. They were unable to do so without the northeastern Republicans.

GOP leaders had intended to bring the re-written deficit reduction bill to the House floor Thursday afternoon. But many of the moderates who forced the end of the drilling measure also oppose the deficit bill's provisions to curb Medicaid growth, change food stamp eligibility and trim student loan subsidies.

"I have to represent my district," said Rep. Tim Johnson, R-Ill., who represents farmers opposed to cuts in commodity payments as well as the University of Illinois campus, which is upset about cuts to student loans. "At this point, I am very, very skeptical."

The Senate last week passed a different version of the bill that would curb the automatic growth of federal spending by $35 billion through the end of the decade. But with Senate Republicans debating new tax cuts, Democrats argue the deficit reduction plan is just a chance to cut spending in order to give breaks to the wealthy.

"Republican moderates are still being asked to walk the plank for a party that has alienated the American public by demanding tax cuts for those who don't need help by cutting education and health programs for those who do," said Rep. Edward Markey, D-Mass.

The House plan would cut more through social services. It will still grow much faster than inflation even after beneficiaries face increased co-payments and the likely loss of some benefits.

"We are not cutting Medicaid for those truly in need," said Rep. David Dreier, R-Calif.

Top Republicans such as Budget Committee Chairman Jim Nussle, R-Iowa, and Majority Leader Roy Blunt, R-Mo., worked into the night Wednesday refining the bill in an attempt to bring uneasy lawmakers on board. Florida Republicans were especially active, helping kill the offshore drilling plan and loosening proposed restrictions on food stamp benefits for legal immigrants.

The decision on the Arctic refuge was a big setback for those who have tried for years to open a coastal strip of the Arctic National Wildlife Refuge, or ANWR, to oil development. It was a victory for environmentalists, who have lobbied hard against drilling. President Bush has made drilling in the Alaska refuge one of his top energy priorities.

White House press secretary Scott McClellan said Thursday the president was pleased that Congress was moving forward with deficit-reduction packages but that he still strongly supports opening up a small portion of ANWR to environmentally responsible exploration.

"We continue to urge passage of that initiative," McClellan said. "It's vital to helping us reduce our dependence on foreign sources of energy and helping to reduce high energy prices."

Protection of the Alaska refuge from oil companies has been championed by environmentalists for years. The House repeatedly has approved drilling in the refuge as part of broad energy legislation, only to see the effort blocked each time by the threat of a filibuster in the Senate.

The budget bill is immune from filibuster, but drilling proponents suddenly found it hard to get the measure accepted by a majority of the House. Twenty-five Republicans, led by Rep. Charles Bass of New Hampshire, signed a letter asking GOP leaders to strike the Alaskan drilling provision from the broader $54 billion budget cut bill.

GOP leaders who prefer to include ANWR in the deficit reduction bill say they have not given up hope yet. Marnie Funk, a spokeswoman for Senate Energy Committee Chairman Pete Domenici, R-N.M., said Domenici considers the Senate-approved ANWR provision "one of the most critical components" in the budget package.

The food stamps change was the only concession to lawmakers upset with a spate of cuts to social programs. GOP leaders bowed to pressure from Cuban-American lawmakers from the Miami area to loosen new restrictions on food stamps benefits for legal immigrants.

Immigrants who are disabled, over the age of 60 or applying for citizenship would be exempt from proposed rules extending the waiting period for food stamp eligibility from five to seven years.

FOX News' Major Garrett and Jim Mills and The Associated Press contributed to this report.