Senate Democrats increasingly unnerved by the disastrous rollout of President Obama’s signature legislative accomplishment are bringing top White House officials to Capitol Hill tomorrow for a major meeting on the topic.

The summit comes as a proposal from Senator Mary Landrieu of Louisiana to amend Obamacare to allow people to stay on their health-care plans is gaining momentum and House Republicans are preparing a test of Democratic unity with a vote on their own bill Friday.

Today Senator Angus King of Maine, an independent who caucuses with the Democrats, told National Review Online he is “inclined to support” Landrieu’s bill, signaling he may become the latest co-sponsor. Numerous other Democrats interviewed after a caucus lunch today said they are reviewing the bill and keeping their options open ahead of the meeting tomorrow.

Senator Tom Carper of Delaware said he expects White House chief of staff Dennis McDonough will lead the White House presentation. Top Health and Human Services Department officials may also attend.

Majority Leader Harry Reid said Obama personally assured him in a phone call last night that Obamacare’s many problems would be fixed.

“I had quite a long conversation, at least for me, I don’t have many long conversations, with the president last night. It was kind of late, I was surprised when he called me so late. But yes, I feel very comfortable after having that conversation last night. It will be fixed,” Reid said.

On the House side, Democrats are facing a tough vote Friday on a bill to allow people to stay on their current health-care plans, but Landrieu — who is pushing her own, similar proposal, threw cold water on the House bill.

“That bill guts the Affordable Care Act. It does not fix it; it guts it, and I don’t support it and would urge the Democrats in the House not to support it,” she told reporters.