The Senate Budget Committee will mark up the measure on Thursday as the House Budget panel completes its own amending process this week.
Both budget blueprints are expected on their respective floors next week for amendments and votes.
President Obama is set to release his budget sometime during the week of April 8, more than two months behind schedule.
"This budget makes tough spending cuts and leaves no sacred cows, but it also makes sure that seniors and the middle class aren’t forced to bear the full burden of deficit reduction by eliminating wasteful loopholes through tax reform, so that the wealthiest Americans pay their fair share," the White House statement said.
"Republicans and Democrats have now put their plans on the table. And while there are differences, both sides share some common goals," the statement said.
"The president looks forward to seeking compromise and common ground with Congress so we can grow the economy, create jobs and cut the deficit in a balanced way."
Obama is spending three days this week on Capitol Hill to meet with Democrats and Republicans on both sides of the Capitol to discuss a broad range of issues, including budget matters.