Sources tell CBS News that President Obama has given Vice President Joe Biden the greenlight to mull a White House run.

The two had lunch together Monday afternoon at the White House before Mr. Obama left for Las Vegas.

Press Secretary Josh Earnest said at the White House briefing Monday that Mr. Obama believes putting Joe Biden on the ticket in 2008 was the smartest decision he's made in politics.

"I think that should give you some sense of the president's view of Vice President Biden's aptitude for the top job," said Earnest.

That wasn't an endorsement. A Biden candidacy could be awkward for the president -- with his former Secretary of State, Hillary Clinton the Democratic frontrunner. Still, Earnest also made no guarantee that Mr. Obama would remain neutral in the primary campaign, telling reporters, "I wouldn't rule out an endorsement."

The vice president's intensifying deliberations are tied to growing concerns among donors and top Democrats that the controversy over Clinton's private e-mail server is snowballing.

In addition to Sen. Warren, Biden and close advisers have been reaching out to supporters in early voting states. They believe they can raise roughly $25 to $30 million over the next six months, tapping into the scores of major donors that are still on the sidelines.

According to a CBS News analysis, out of the nearly 770 people who were top Obama fundraisers in 2012, a fraction -- at least 51 -- have committed to bundling large sums of money for Clinton.

But a Biden candidacy wouldn't be free of his trademark gaffes, and among other considerations that weigh against him are the fact that he's run twice before, and now, at 72 years of age, he would be the oldest person ever elected president.

Aides expect Biden to make a decision by the end of September. A Democratic donor who speaks with Biden regularly and would support a Biden campaign told CBS News family considerations remain absolutely central to his decision. They're still mourning the death of Biden's eldest son, Beau, who is said to have urged his father to run.

And Biden and his family - including his wife Jill and Beau's widow and their children - are not yet sure if they are emotionally prepared for what is sure to be a grueling campaign. But the donor added that Biden is "more comfortable today than he was a month ago."

CBS News' Steve Chaggaris contributed to this report.