WASHINGTON — The White House is downplaying its draft immigration proposal as merely a backup plan if lawmakers don’t come up with an overhaul of their own. It won’t be necessary, Republican and Democratic lawmakers alike are telling the Obama administration.

White House chief of staff Denis McDonough said Sunday that President Barack Obama wants to “be prepared” in case the small bipartisan group of senators fails to devise a plan for the estimated 11 million illegal immigrants in the United States. In response, lawmakers assured the White House they are working on their own plan — and warned that Obama would be heading toward failure if the White House gets ahead of them.

“We will be prepared with our own plan if these ongoing talks between Republicans and Democrats up on Capitol Hill break down,” McDonough said, adding he’s optimistic they would not crumble.

But he was equally realistic about the fierce partisanship on Capitol Hill.

“Well, let’s make sure that it doesn’t have to be proposed,” McDonough said of the president’s pitch, first reported on USA Today’s website late Saturday.

Even so, the administration is moving forward on its own immigration agenda should one of Obama’s top priorities get derailed.

The administration’s proposal would create a visa for those in the country illegally and allow them to become legal permanent residents within eight years. The proposal also requires businesses to know the immigration status of their workers and adds more funding for border security.

It drew immediate criticism from Sen. Marco Rubio, R-Fla., one of the eight lawmakers searching for a comprehensive plan.

“If actually proposed, the president’s bill would be dead on arrival in Congress, leaving us with unsecured borders and a broken legal immigration system for years to come,” said Rubio, who has been a leading GOP spokesman on immigration.

Many of the details in the administration’s draft proposal follow the broad principles that Obama previously outlined. But the fact the administration is writing its own alternative signaled Obama wants to address immigration sooner rather than later and perhaps was looking to nudge lawmakers to move more quickly.

The tactic could complicate the administration’s work with Congress.

David Axelrod, who was a senior adviser to Obama’s re-election campaign, acknowledged Monday that it likely was a mistake for news of the Obama immigration plan to be made public.

Appearing on MSNBC, Axelrod said in an interview from Chicago that “the mistake here was to disseminate it so widely within the administration” and said he believes that White House officials would “take it back” if they could.

Republican Rep. Paul Ryan, the Wisconsin lawmaker who was his party’s vice presidential nominee last year, said the timing of the leak suggests the White House was looking for “a partisan advantage and not a bipartisan solution.”

“Leaking this out does set things in the wrong direction,” said Ryan. “There are groups in the House and the Senate working together to get this done and when he does things like this, it makes that much more difficult to do that.”

Freshman Rep. Joaquin Castro, D-Texas, called the leaked plan “incomplete” and said both parties in Congress and the White House need to work together on a solution.

“It hasn’t happened yet. It will happen before something is acted upon and certainly before something is passed,” he said.

Republican Sen. John McCain predicted the administration’s efforts would come up short if the White House went forward with a proposal, and he encouraged the White House to give senators a chance to finish their work.

McCain, the Arizona senator whose previous efforts at an immigration overhaul ended in failure in 2007, predicted the White House proposal’s demise if it were sent to Congress. He strongly urged the president to pocket the drafted measures.

“I believe we are making progress in a bipartisan basis,” said McCain, who is in the Senate group working on legislation.

And Democratic Sen. Chuck Schumer, who met with Obama on Wednesday at the White House to discuss progress, urged his allies in the administration to give a bipartisan group of eight lawmakers the time to hammer out a deal on their own.

Schumer, a New York Democrat and a close ally of the White House, said he has not seen the draft proposals but, along with the Democrats working on a compromise, met with Obama this week to talk about progress being made on Capitol Hill.

Schumer acknowledged that a single-party proposal would have a much more difficult time becoming law and urged the bipartisan group of senators to keep meeting to find common ground.

“I am very hopeful that in March we will have a bipartisan bill,” Schumer said. “And, you know, it’s obvious if a Democrat — the president or anyone else — puts out what they want on their own, (it) is going to be different than when you have a bipartisan agreement. But the only way we’re going to get something done is with a bipartisan agreement.”

McDonough appeared on ABC’s “This Week,” NBC’s “Meet the Press” and CBS’ “Face the Nation.” Ryan and Castro spoke to “This Week.” McCain spoke to “Meet the Press.” Schumer appeared on CNN’s “State of the Union.”