Senate Democrats will hold a closed-door full caucus meeting Thursday with Obama administration officials to discuss their growing concerns with problems in the health care law, Majority Leader Harry Reid said Wednesday.

The Nevada Democrat also said that President Barack Obama called him late Tuesday night to discuss an array of issues, including the problems with the health care law and its rollout.

“There are many questions about health care, and that’s why tomorrow we’re having a full caucus … the White House is going to be there,” Reid said.

The majority leader declined to say whether he would bring to the floor amendments from Democratic senators that would make changes to the Affordable Care Act. Some of the key changes being proposed even by Democrats include bills to delay the individual mandate penalty payments as well as legislation to grandfather in individual’s old insurance plans that likely would get cancelled in the reformed system.

The bill to grandfather in existing health care plans that don’t meet ACA standards — proposed by Sen. Mary L. Landrieu, D-La. — has been picking up a little steam among Democrats in recent days, with Sens. Dianne Feinstein of California and Jeff Merkley of Oregon announcing their support this week. The measure is aimed at making good on Obama’s promise that people who liked their existing health insurance plans could keep them under the Obamacare law. That has turned out to not be true for millions of Americans.

On Wednesday, White House spokesman Jay Carney said the president shares the goal of the Landrieu bill, but he stopped short of endorsing it.

“We’re going to work with her and work with others,” Carney said.

Steven T. Dennis contributed to this report.