A House Armed Services Committee spokesman said Pentagon officials said the budget would be submitted April 8, The Hill reported Friday.
Congressional sources said last week they were told the Obama's proposal would be submitted March 25.
By law, the president must submit a budget by the first Monday in February, but Obama has met the deadline only once.
During Friday's media briefing, deputy press secretary Josh Earnest declined to comment, saying, "I don't have a budget date to announce to you.
"As we've talked about for some time, the budget has been delayed because of some of the impediments frankly to formulating a budget that have been thrown in the path of those who are working on it," Earnest said. "We had a fiscal cliff debate that lasted through the end of last year. Certainly the implementation of the sequester has affected the ability of the administration to put together our budget proposal, but that's something that people are hard at work on."
Earnest said the White House would have more information in the coming weeks about the budget and how it reflects Obama's "policy priority is strengthening our economy for the middle class."
Concerning the debt ceiling, House Speaker John Boehner, R-Ohio, said any increases in the limit must be matched by spending cuts, even if Obama mends fences with Republicans.
The Treasury is expected to reach its $16.4 trillion borrowing limit in May.
Boehner said he welcomed Obama's new outreach effort, even though it sidestepped him and other congressional leaders and was directly with rank-and-file lawmakers.
"I think it's a sign, a hopeful sign," Boehner said. "And I'm hopeful that something will come out of it."
He said he still wouldn't support raising the debt ceiling without matching spending cuts.
Obama and some GOP members have said they'd be willing to talk about cutting the deficit through an approach that would include overhauling the tax code and slowing the growth of entitlement spending on programs such as Medicare and Social Security.
"There was a common belief that entitlements need to be reformed and the tax code needs to be modernized," Sen. Lindsey Graham, R-S.C., told reporters, after dining with Obama Wednesday.
But "the details may trip us up," Graham said.
Potential obstacles include the White House push for tax changes that result in a net rise in revenue, which many GOP lawmakers oppose. At the same time, many Republicans want to overhaul entitlement programs in ways that are more drastic than Democrats prefer.