WASHINGTON — Republicans and Democrats alike on Sunday predicted President Barack Obama would fail if he pushed forward with his own effort to overhaul the nation's immigration system and urged the administration to hold off while lawmakers work on a bipartisan measure.Republican Sen. John McCain predicted the administration's efforts would come up short if the White House went forward with a proposal to put the estimated 11 million illegal immigrants in the U.S. on a long pathway to citizenship. 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.Obama's newly appointed top aide, chief of staff Denis McDonough, said the White House would only send its plan to Congress if the lawmakers stumble in their efforts and cast its efforts as a backup plan."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."We will be prepared with our own plan if these ongoing talks between Republicans and Democrats up on Capitol Hill break down," McDonough said in a second interview, adding he's optimistic they would not crumble.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."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 is among the eight lawmakers searching for a comprehensive plan.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 potentially complicates the administration's work with Congress.Republican Rep. Paul Ryan, the Wisconsin lawmaker who was his party's vice presidential nominee last year, said the timing of the leak suggested 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, who could be a serious contender for his party's presidential nomination in 2016. "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.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 and give senators a chance to finish their work."I believe we are making progress in a bipartisan basis," McCain, who is among the Senate group working on legislation, said.Schumer, a New York Democrat and a close ally to 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."Sen. Rand Paul, R-Ky., suggested Obama's proposed plan was going nowhere but added that his party was evaluating its relationship with Hispanic voters, who supported Obama in November with 71 percent of their votes."I think people want a little different face on immigration, frankly," said Paul, who is also considered among the 2016 presidential hopefuls. "They don't want somebody who wants to round people up, put them in camps and send them back to Mexico."The Associated Press, relying on a CQ Roll Call transcript that was distributed after "Fox News Sunday" and omitted the word "don't" in that quote, initially reported that Paul saw his party as in favor of such efforts to deport immigrants. The AP's subsequent review of an audio recording of the broadcast confirmed the missing word.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."