The act, passed to end racist voting practices, had been set for a House vote Wednesday on its renewal, with Republican and Democratic leaders behind it.
It was unclear whether the objections could be resolved this year, said the aide, who spoke on condition of anonymity because the decision had not yet been made public.
The temporary portions of the 1965 law expire next year, and it was unclear whether the objections could be resolved during this year of midterm elections, in which House leaders of both parties hope to use the bill to advance their prospects at the polls.
Leaders of both parties support the legislation, which was approved by the Judiciary Committee on a 33-1 vote. Despite their support, controversy has shadowed the legislation 40 years after it first prohibited policies that blocked blacks from voting.
Several Southern Republicans, led by Rep. Lynn Westmoreland, had worked to allow an amendment that would ease a requirement that nine states win permission from the Justice Department or a federal judge to change their voting rules.
The amendment's backers say the requirement unfairly singles out and holds accountable nine states that practiced racist voting policies decades ago, based on 1964 voter turnout data: Alabama, Alaska, Arizona, Georgia, Louisiana, Mississippi, South Carolina, Texas and Virginia.
Westmoreland says the formula for deciding which states are subject to such "pre-clearance" should be updated every four years and be based on voter turnout in the most recent three elections.
"The pre-clearance portions of the Voting Rights Act should apply to all states, or no states," Westmoreland said. "Singling out certain states for special scrutiny no longer makes sense."
The amendment has powerful opponents. From Republican and Democratic leaders on down the House hierarchy, they argue that states with documented histories of discrimination may still practice it and have earned the extra scrutiny.
The overwhelming support for the bill was foreshadowed by the Judiciary Committee's 33-1 vote last month to report the renewal to the full House.
"This carefully crafted legislation should remain clean and unamended," Rep. John Conyers, who worked on the original bill, which he called "the keystone of our national civil rights statutes."
By his own estimation, Westmoreland says the amendment stands little chance of being adopted.
The House also could bring up an amendment that would require the Justice Department to compile an annual list of jurisdictions eligible for a "bailout" from the pre-clearance requirements.
That amendment, too, has little chance of surviving the floor debate, leaving the underlying bill likely to pass the House. The Senate is scheduled to consider an identical bill later this year.