"It is, by far, the president's preference that the Senate process move forward, that the bipartisan group of eight have success, and that they produce a bill that wins the support of Democrats and Republicans in Senate," White House spokesman Jay Carney said.
Senate aides said privately that bipartisan negotiations are in a good place and did not feel as though the disclosure of details in Obama's draft bill would disrupt their progress. In fact, Obama's backup bill could end up spurring GOP lawmakers to rally behind a similar congressional plan rather than support legislation attached to the president.
While they differ on some key details, both sides are contemplating legislation that would provide a pathway to citizenship for most of the 11 million illegal immigrants already in the U.S., tighten border security, crack down on businesses that employ illegal workers and strengthen the legal immigration system.
Rubio, a rising Republican star and favorite of his party's conservative wing, has particular incentive to disown Obama's proposals.
As one of his party's leading voices on immigration, Rubio will be called on to sell other conservatives on any deal and knows that doing so will be harder if that deal has the president's name attached to it. He'll also have to convince Republicans that a bipartisan Senate agreement would be more conservative than what Obama would propose on his own.
Rubio's office, trying to further distance itself from the White House, insisted that the senator's team had not been in talks with the administration on immigration. But Rubio spokesman Alex Conant later backed away from that statement after senior administration officials said representatives from Rubio's office had been part of five bipartisan immigration meetings with the White House.
The White House has insisted it did not intentionally leak details of its immigration plan, which circulated widely at key government agencies. Top Obama aides tried to clear up the mess over the weekend, making apologetic calls to the offices of the eight senators at the center of the Capitol Hill negotiations.
Obama officials say the documents represent draft proposals, not a final bill. The president and his aides have repeatedly said publicly that the White House was readying legislation and would submit it to Congress if the Senate process stalls.
The draft White House proposal and the principles outlined by the Senate group overlap in many areas, though there are some key differences.
The administration's draft proposal would create a visa for those in the country illegally and allow them to become legal permanent residents within about eight years as part of a broader pathway to citizenship. The Senate group is looking at a 10-year timeline before people already in the U.S. illegally could get green cards.
While Obama's proposal calls for more funding for securing the border, it does not make border security a pre-condition for opening a pathway to citizenship. The Senate group's principles would require a border security trigger, though it's unclear how they would define a secure border.
Rubio's office has also criticized the president's proposals for not including a guest worker program or a plan for dealing with the future flow of immigrants.
Officials say the White House has not set a deadline for when the president would choose to abandon the Senate process and send his bill to Capitol Hill. Senate lawmakers have raised the prospect of drafting a bill next month.
Hanging over the entire immigration debate in Washington is a changed political landscape that gives Hispanics more influence in national politics than ever before. Hispanics made up 10 percent of the electorate in the November presidential election and Obama won more two-thirds of their votes, causing many Republican lawmakers to rethink their opposition to immigration reform.
Immigration advocates have vowed to keep reminding GOP lawmakers of the growing political power of Hispanic voters.
"You can choose not to do it, you can choose inaction, but keep in mind that the Latino community is not going to forget," said Eliseo Medina, an immigration advocate and labor leader at the Service Employees International Union.
"If the Senate blocks it, then get prepared for 2014," he added, referring to next year's congressional elections.