(FoxNews) – The Senate battle may be over for now, but Republicans are vowing the war is not won quite yet.

Congress may be gone for several weeks enjoying a winter holiday, but Republicans have vowed to keep up the pressure on Democrats who succeeded in getting their Senate health insurance overhaul bill passed before Christmas — if just barely.

Several GOP lawmakers say they are still hoping to peel back support for the bill among budget-minded Democrats who are certain to hear from furious constituents over the long break about the overwhelming cost of the $871 billion, 10-year legislation.

“This is not over,” Sen. John Barrasso, R-Wyo., told Fox News. “We are going to work, asking people to talk to their senators, make them face the music. The American people don’t support this effort for government to run health care.”

“I guarantee you, the people who voted for this bill are going to get an earful when they get home, when they finally get home for the first time since Thanksgiving,” said Senate Minority Leader Mitch McConnell. “They know there is widespread opposition to this monstrosity. I want to assure you, Mr. President, this fight isn’t over. In fact, this fight is long from over.

Republicans say they will try to stall the bill from moving forward using several means. Already a group of GOP state attorneys general are building a case on the constitutionality of the legislation.

Sen. John McCain, R-Ariz., said the favoritism shown to certain senators in exchange for their votes should raise constitutionality questions.

“I have never seen anything quite like this. I believe that the ‘corn husker kickback’ will rank up there with the bridge to nowhere as a tipping point,” he said, comparing Nebraska Sen. Ben Nelson’s acceptance of a deal to have his state never pay Medicaid to the billions in cash offered Alaska for a bridge to an island populated by 50 people.

“We have got to stop this way of doing business in Washington. … People have lost trust and confidence in the way we do business. And I think this latest thing is going to throw gasoline on the tea party fires,” he said.

Before lawmakers were to depart for their vacation after the vote on a debt ceiling hike,Republicans did succeed in forcing one minor setback for Senate Majority Leader Harry Reid.

Reid had wanted to assign conferees to meet with House negotiators on a compromise between the two versions of the bill. Democrats had hoped to begin negotiations as early as next week, though the House doesn’t return officially until Jan. 12 and the Senate until Jan. 19.

But Reid’s effort was dashed by Republicans who put the leader on notice that they would object to the appointment of conferees, and that would have delayed the Senate’s recess, something no one wanted on Christmas eve.

House and Senate Democrats do have parliamentary avenues to get around the objection. The House and Senate can play ping-pong with the bill, where the Senate pings the bill over to the House and it makes changes and then the House pongs it back over to the Senate for another round.

This congressional table tennis continues until both bodies have adopted the same piece of legislation. That, however, could take longer than the administration had hoped.

Before they left, Republicans also prevented several of Obama’s nominees from getting unanimous approval for a judgeship, an assistant attorney general post and several Treasury spots.

Already some interest groups are forming protests to the legislation. One ardent pro-life group said it would protest at Catholic in Hawaii, where the Obamas are vacationing until after the New Year, and in Washington, D.C. on Saturday and Monday.

“President Obama is already spending our money to promote child-killing in Africa and forced abortion in China. We are calling on him to refuse any ‘health care reform’ which mandates, either directly or indirectly, the use of taxpayer dollars for the procurement of abortion,” said Gary Boisclair, leader of the Honolulu affiliate of Washington D.C.-based Insurrecta Nex, an outgrowth of Operation Rescue.

“Abortion is tyrannical; it is nothing but the murder of innocent children,” Boisclair added.

White House officials said they expect the president will spend his vacation recharging before heading back to the mainland to start promoting final passage of the bill. Spokesman Bill Burton said the two pieces of legislation are “95 percent similar” and the president will be “actively working to iron out the rest of the differences and get a bill passed and signed.”

However, Burton could not say whether Obama plans to campaign for it around the nation.

“The president has been very actively talking to the American people about it. You can bet that he’ll continue to do that in January — but I don’t have anything on that level of specificity as to whether or not he’s going to go out and actually do events and that sort of thing on health care reform,” he said.

Before his departure, Obama hailed the legislation as the biggest social sea change since the passage of Medicare and Social Security.

In a White House blog, Communications Director Dan Pfeiffer said that Republicans already have tried to stop the bill by stonewalling, but their claims of exclusion are as empty as their threats to stop the bill.

“Today’s Republican talking point of the day is that the historic health reform bill passed today represents the first major piece of social legislation to be passed without a single vote from across the aisle. Well that may be true. But it’s not a commentary on this bill. It’s a commentary on the Republican Party, whose leaders made a determination that they were going to put party over progress. That’s never happened before when the nation took on big challenges,” he wrote.