The bill passed the House of Representatives 279-144 with mostly Republican support.
Republican support for the bill was motivated by a desire to not oppose a tax cut in an election year.
Doing so with Republican support would also allow him to claim a bipartisan victory.
Republican support is needed, she said, because some Democrats also support further restrictions on abortion.
The tax relief seemed likely to win more Republican support for the underlying tobacco legislation.
"Without Republican support, there's not much that can be done."
The shift, however, left Democrats with an 18-12 majority, allowing them to pass increases to taxes and fees without Republican support.
Enough Democrats oppose the measure that it cannot be passed without Republican support.
They said they feared that such a delay might build more Republican support for the measure.
But he also needs Republican support for his next round in the budget process.