The US Senate has passed legislation that would increase tobacco taxes to pay for an expanded children's healthcare insurance programme.
Mr Bush believes the bill extends the programme too far
The Senate voted by 68-31 to provide an extra $35bn (£17bn) to insure some 10 million children.
The House of Representatives has already passed its own version.
President George Bush opposes the move, arguing that it takes the programme beyond its original purpose of insuring children in low-income families.
The Senate and the House of Representatives must now reconcile their versions of the bill before sending it to President Bush after Congress's summer recess.
The Senate bill would increase spending on the State Children's Health Insurance Programme (SCHIP) by $35bn (£17bn) over the next five years.
This would expand health coverage to include 3.2 million more children and would ensure continuing insurance for the 6.6 million children already in the programme, Senate Democrats said.
It would be paid for by increasing federal taxes on cigarettes from 39 cents a pack to $1 (50p).
"Covering these children is worth every cent," said Republican Sen Orrin Hatch.
The House version of the bill envisages a $50bn increase for SCHIP, which would also be paid for by tobacco tax increases but also by cuts in government subsidies to private insurers offering health care plans for the elderly and disabled.
Given the differing scope of the two versions, reconciling them will prove a challenge.
"It's going to be difficult. But we're talking about kids and that's the dynamic that holds us together," said Democratic Sen Max Baucus.
The programme is due to expire on 30 September.
President Bush has threatened to veto the legislation, which he argues would expand a programme that has already gone beyond its original remit.
It was set up to help working families who could not afford private health insurance but who earned too much to qualify for Medicaid - the government health care programme for the poor.
A White House statement said the Senate bill "essentially extends a welfare benefit to middle-class households".
Republican Sen Trent Lott voiced concerns that SCHIP was ballooning.
"The problem here is we are exploding the programme. The ultimate goal is for all children to be covered by 'Mother Washington'," he said.
If Mr Bush were to veto the legislation, the programme's future could become an issue in the 2008 presidential campaign amid a broader debate about universal health care coverage, correspondents say.