Gaby Pacheco, a vocal immigrant activist, accepted a tantalizing invitation last week from an unlikely source: Republican Sen. Marco Rubio wanted her to help craft a bill that could legalize the children of some illegal immigrants.

Two hours later, Pacheco and other activists got a different pitch from their more familiar White House allies. Be wary of Rubio and his plan, two of President Obama’s top advisers told them in a meeting. It wouldn’t go far enough and wasn’t likely to succeed.

The group was polite but noncommittal. “We’re not married to the Democratic or Republican parties,” said Pacheco, 27. “We’re going to push what’s best for the community.”

The events of that day illustrated how the new effort by Rubio (Fla.) has upended the immigration debate in Washington, exposing tensions in both parties as Obama and the GOP assess how the issue might sway the crucial Hispanic vote in November.

In recent days, Rubio has quietly reached out to a number of immigrant advocates who are usually White House allies but have grown frustrated with some of the president’s policies. Some of the activists say they are open to Rubio’s effort — even though it would stop short of a provision in the Democratic-backed Dream Act to create a path to citizenship — because it would at least provide some relief to people at risk of being deported.

Rubio has not put his plan on paper, but his office describes it as an “alternative” to the Dream Act that would legalize certain young people who came to the United States while they were children. The measure would grant non-immigrant visas so qualified young people could remain in the United States for college or to serve in the military.

The plan puts Obama in a box. Democrats are reluctant to see Rubio’s efforts as anything other than a political gambit to repair his party’s tarnished image with Hispanics and boost his own profile as a potential vice-presidential pick or future White House contender.

But if Obama does not at least try to work with Rubio, he could risk losing a centerpiece of his appeal to Hispanic voters — that he is their fiercest ally in Washington and that the GOP is to blame for lack of action on fixing the country’s immigration ills.

White House resistance to Rubio threatens to escalate criticism from Obama allies frustrated that he was unable to deliver on a broad immigration overhaul and angry that his administration has deported more than 1 million illegal immigrants.

A White House official who spoke on condition of anonymity called it “ludicrous” to suggest that the president would be an obstacle to helping the young people or their advocates. The official noted that Obama would happily have signed the Dream Act into law in 2010 had Republicans not blocked it and that he remains in favor of a broader plan that would create a path to citizenship for many of the 11 million to 12 million people in the United States illegally.

The official said that the president welcomed any serious effort from Republicans to forge a bipartisan approach but that it was impossible to fully judge Rubio’s plan until it appears in writing as a bill.

Obama seemed to disparage the Rubio effort during an interview this month on the Spanish-language network Telemundo. “This notion that somehow Republicans want to have it both ways, they want to vote against these laws and appeal to anti-immigrant sentiment . . . and then they come and say, ‘But we really care about these kids and we want to do something about it’ — that looks like hypocrisy to me,” Obama said.

The issue also presents a quandary for likely GOP nominee Mitt Romney, who has alienated many Hispanic voters with his hard-right positions and rhetoric on immigration during the Republican primary campaign.

He now must weigh how to undo the damage without angering conservatives who are on the lookout for a flip-flop by a candidate known for his evolving views.

At a Monday campaign event with Rubio, Romney did not take a position on the plan.

“I’m taking a look at his proposal,” Romney said. “It has many features to commend it, but it’s something that we’re studying.”

Several conservatives have already blasted Rubio’s plan as a form of “amnesty,” but aides to the senator say he is lobbying key players and media personalities on the right to hold their fire.

Many Democrats have dismissed the push by Rubio, the son of Cuban immigrants who was elected in 2010 as a conservative darling after adopting hard-line positions on illegal immigration. Some critics on the left say his proposal would create a second class of Americans, permitted to live in the United States but unable to achieve the full rights of citizenship.

But his efforts appear to be further driving a wedge between Obama and his restive Hispanic activist supporters.

The senator conferred Wednesday afternoon with several leading members of the Congressional Hispanic Caucus, for example, including Rep. Luis V. Gutierrez (D-Ill.), one of the most vocal critics of Obama’s deportation policies.

Last week, Rubio sat at a dinner party beside Janet Murguia, president of the National Council of La Raza, one of the country’s most prominent Hispanic advocacy groups, and the two discussed ways to work together on policy.

“It’s clear that there wouldn’t be an effort to be talking about this right now if it weren’t for Senator Rubio engaging on this,” Murguia said. “We need to know whether the president can use this as an opportunity.”

Rubio’s outreach to Pacheco — who was brought to the United States illegally when she was 8 — and other young undocumented immigrants came after they had been asking for months without success for a chance to meet with Obama. The senator first called Pacheco on her cellphone, and the two spoke for about a half-hour. He later met with a small group at Miami-Dade College.

“He said, ‘If you feel at any point that this is something you guys cannot support, let me know,’ ” Pacheco recalled.

The president’s challenge has been evident in recent days during tense encounters between top White House aides and Hispanic leaders, who have continued to press for the president to simply sign an executive order preventing the deportations of any people who would qualify for the Dream Act. In one heated session last week between Congressional Hispanic Caucus members and domestic policy adviser Cecilia Munoz, Rep. Lucille Roybal-Allard (D-Calif.) grew so frustrated that she walked out, according to people familiar with the meeting.

In their meeting with Pacheco and other young activists, Munoz and senior White House adviser Valerie Jarrett offered warnings that going along with Rubio’s plan put at risk other efforts to pass the full Dream Act with a path to citizenship. They told the activists that Rubio had not demonstrated he could win support from fellow Republicans and that the president would use his clout to push an immigration plan next year. “They said, ‘Be careful we’re not lowering the bar. Citizenship is important,’ ” Pacheco recalled.

But Pacheco, who remains undocumented even after graduating from college, said Obama should see the situation as more urgent. “We’re at a point of desperation, at a point where we cannot continue to live the way we’ve been living,” she said.