The Senate approved the budget deal in a 64-36 vote.
“This technical error can, will and should be addressed," the senator said.
"We strongly support it," senior White House adviser Valerie Jarrett said.
The budget deal is expected to pass the Senate with bipartisan support later Wednesday.
Sen. Jeff Sessions (R-Ala.) tried to bring up an amendment to stop a $6 billion cut in military retiree benefits, but didn’t have the votes to set aside the pending amendments.
“The legislation before us today now is brought forward in a way that will not allow any amendments,” Sessions said Tuesday. “Nobody can get an amendment to fix this part of the legislation that plainly needs fixing.”
He said the GOP will make demands in exchange for increasing the debt ceiling this spring.
Sen. John McCain (R-Ariz.) said Tuesday that it “lacks some intellectual integrity” to vote against the bipartisan budget deal without having an alternative to avert another government shutdown.
“I’d like to know what we do in order to avoid another shutdown of the government,” McCain said on the Senate floor. “To somehow vote against it without an alternative to keep the government from shutting down, I think lacks some intellectual integrity.”
A final vote on the deal will come on Wednesday.
Rep. Paul Ryan suggested tying approval of the oil pipeline to raising the debt ceiling.
Sen. Tom Coburn lists 100 government spending decisions that wasted $30 billion.