If accepted, the compromise would break the logjam within the House Democratic caucus on the massive $183 billion bill to fund the wars in Iraq and Afghanistan.
Last week a group of fiscally conservative Blue Dog Democrats delayed consideration of the supplemental over the veterans' benefits issue, arguing that the cost of the expansion of education benefits to returning war veterans was not offset in the bill.
Although specific details of the proposal were not available, the aide indicated it would be a .5% tax on income for couples over $1 million, which would raise $54 billion over 10 years.
The Congressional Budget Office estimates that the expansion of veterans' education benefits would cost $51.8 billion over the next 10 years.
As the House Democratic leadership met on Tuesday night to discuss the plan, there was no word if the Blue Dogs would accept the compromise and drop their objections to the supplemental.
Democratic Rep. Allen Boyd of Florida, a co-chair of the Blue Dogs, said he would support the package with these offsets included. He and a handful of other Blue Dogs were threatening to block consideration of the legislation, which will come to the floor as a series of amendments, unless leaders agreed to pay for the education benefits for veterans.
The surcharge proposal was the fruit of staff negotiations over the weekend between leadership and aides to prominent Blue Dogs, Boyd said, and the Florida Democrat believes most of the budget hawks in his party will support the package as a result.