The vote was 5 to 3, with the court’s liberals in dissent.
President Trump’s third nominee secured her seat on the court with only Republican votes.
The president’s first-term judicial legacy, primarily engineered by Sen. Mitch McConnell and his singular focus on the courts, culminates Monday with the expected confirmation of Amy Coney Barrett to the Supreme Court.
The Alaska Republican, who had said the Senate should not vote on a new justice so close to the election, said she wouldn’t hold her opposition to the process against Barrett.
The nominee refused to say at confirmation hearing whether the landmark same-sex marriage case was properly decided. But a pending case could make views more transparent.
Lower courts had said that local jurisdictions that want to offer accommodation to the elderly and disabled should be able to do so.
The 22-member Senate Judiciary Committee is scheduled to vote Thursday on President Trump’s nominee, who was expected to win approval on a party-line vote.
The court’s action carried outsize importance because of Pennsylvania’s pivotal role in the presidential election.
The Trump administration asked the court to intervene in both cases because lower courts have ruled against its policies.
A lower court blocked the plan, which would have the effect of shifting both political power and federal funds away from urban states with large immigrant populations.
Liberals were particularly irate at Feinstein’s praise of Republicans for their handling of Trump Supreme Court nominee Amy Coney Barrett’s confirmation hearings.
“We have the votes,” said Majority Leader Mitch McConnell. The Judiciary Committee will vote next week and the full Senate days later, fulfilling President Trump’s demand for a fast-tracked process.
The Senate Judiciary Committee reconvenes Thursday to hear from supporters and opponents of President Trump’s Supreme Court nominee.
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“The harms caused by rushing this year’s census count are irreparable,” Justice Sonia Sotomayor wrote in her dissent.
Judge Amy Coney Barrett repeatedly avoided weighing in on her personal views of landmark decisions while declining to say whether she would recuse herself from potential 2020 election decisions.
Without comment, justices let stand a lower-court ruling that said individual members did not have legal standing to bring the lawsuit.
The request to the justices is a follow-up to the decision that the president is not immune to investigation while in office.
Monday’s hearing previewed what is expected to be an acrimonious confirmation process.
Her “kind of radical” opinion that some felons have the right to guns had been called an “audition tape” for the high court.