The group's supporters said there could be a way to add at least pieces of the outline to that package. Reid said gang of six member Sen. Mark Warner (D-Va.) will report back to him within the next 24 hours on any provisions that might be able to fit into the Plan B package.
Obama, meanwhile, stopped short of an outright endorsement.
The president praised the group's plan because, he said, it shows Republicans and Democrats can agree on tough spending cuts and increased revenues. He said it would not "match perfectly" with the direction he has been heading but that he and the group are "on the same playing field."
Reid said Tuesday that he expected to hold another negotiating session with House and Senate leaders at the White House on Wednesday. Top Obama advisers also will meet with faith leaders Wednesday to discuss the deficit, Roll Call has learned.
The president also said he still supports the McConnell-Reid fallback plan. "We have to have that fail-safe," he said.
Others explicitly backing the group included Republican Conference Chairman Lamar Alexander (Tenn.) and Health, Education, Labor and Pensions ranking member Mike Enzi (R-Wyo.), as well as rank-and-file Members in both parties.
But Senate GOP support, or even backing from the president whom McConnell said needed to be onboard months ago for the plan to be legitimate does not change the reality of a tea-party-influenced House.
House Republicans so far have been unwilling to consider increased revenues of any kind, let alone the $1 trillion envisioned by the gang.
A spokesman for Speaker John Boehner (R-Ohio) issued a cautious statement.
"This plan shares many similarities with the framework the Speaker discussed with the president, but also appears to fall short in some important areas," the spokesman said.
House Majority Leader Eric Cantor agreed, saying in a statement Tuesday evening that the plan includes some provisions already under discussion with the president but that he is concerned about its revenue target, among other things.
Weve begun reviewing the Gang of Six proposal and while there are still portions that are unclear and need more detail, this bipartisan plan does seem to include some constructive ideas to deal with our debt, the Virginia Republican said.
A GOP aide said House Republicans are pushing for larger structural changes to Medicare and Medicaid and less revenue than the gang's plan calls for, among other differences.
Rep. Kevin Brady (R-Texas) was not upbeat about the group's chance.
"Tax increases aren't going to fly in the House, and I don't believe that is going to change," Brady said.
But Rep. Steven LaTourette (R-Ohio), who is close to Boehner, said he was hopeful that the gang's plan could revive a grand bargain.
"I've seen that the president is excited about it," LaTourette said. "If he's excited, I am excited."
LaTourette said he was fine with new revenue in the plan because it would reduce rates. "What they're talking about is ... simplifying the tax code, closing loopholes. There are some that are going to argue that those are tax increases. I don't buy into that. ... The grand bargain is still there, the president and the Speaker are working on it, and I believe we will have a grand bargain sometime next week."
Terri Henderson, 6, center, whose mother is El Salvador, attends a rally with members of Congress at Union Station's Columbus Circle to announce the Restore Opportunity, Strengthen, and Improve the Economy (ROSIE) Act on July 29, 2014. The legislation provides incentives for government contractors to pay a living wage and other benefits that would help low-income workers.