They urged the administration to hold off while lawmakers work on a bipartisan measure.
Republican Sen. John McCain predicted Sunday that 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.
Sharp shifts in the political landscape have put an immigration overhaul tantalizingly close. Hispanics made up 10 percent of the electorate in the November election, and Obama won about 70 percent of their votes, in part because of the conservative immigration positions staked out by Republicans during their presidential nominating contest.
The general election forced some Republican lawmakers to reconsider their opposition to comprehensive immigration changes, clearing the way for the swift consensus that has emerged between the White House and bipartisan lawmakers in recent weeks.
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, and they would later be eligible to become U.S. citizens. The proposal also includes more funding for border security and requires businesses to adopt a system for verifying the immigration status new hires.
USA Today reported that the bill would require that immigrants pass a criminal background check, submit biometric information and pay fees to qualify for the new visa.
The draft bill drew immediate criticism from Republican Sen. Marco Rubio of Florida, who is considered a potential 2016 presidential candidate.
"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 bipartisan 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 also 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, a Texas Democrat, 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 draft 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."
Republican Sen. Rand Paul of Kentucky 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."