The Trump White House is expecting a vote this week on passing the latest revision of the GOP health care plan as the administration struggles to secure enough support in the House, CBS News correspondent Major Garrett reports.

This comes as CBS News' latest whip count as of Wednesday morning shows at least 21 House Republicans now oppose the revised bill. The GOP can afford to lose only 22 Republican votes for the measure to pass.

Garrett reports that Mr. Trump is set to meet with two influential House Republicans in an effort to turn their no votes into support.

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The hastily arranged meeting between Mr. Trump, Rep. Fred Upton, R-Michigan, and Rep. Billy Long, R- Missouri, is set to find a way to protect the coverage of pre-existing conditions in the new health care bill without losing the votes of conservatives who have just joined in support.

Two senior administration officials tell CBS that the meeting is set to occur in the late morning, and that the White House expects Rep. Upton to come to the meeting with his own amendment on the health care bill to discuss with the president and Rep. Long.

"This is precisely how the process has to work in the House," a senior administration official said. "You nail down the conservatives on the structure of the bill and then you go hunting for the moderates."

If Upton reverses his position on the bill as the White House is anticipating, the bill may have chance to secure the necessary votes to pass.

The future of the health care bill now hinges on whether pre-existing conditions will be guaranteed or a state option in the new plan.

Mr. Trump had promised to "Face the Nation" moderator John Dickerson last week that the coverage of pre-existing conditions would be a guarantee.

But under the new Republican bill, states have the ability to apply for three different waivers from regulations under Obamacare. One of those waivers applies to pre-existing conditions, allowing insurers to use "health status" to set insurance premiums.

A senior administration official said the vote on the latest bill could possibly occur Friday or Saturday, depending on the pace of negotiation and amount of Republican support, as Congress is set to leave Washington for a recess this weekend.

"They have to vote on this before they leave town," the senior official said. "If they don't, it will be over. And they know that."

Although the formal vote has yet to be scheduled, Mr. Trump chided members of Congress just yesterday at a ceremony in the Rose Garden, pressing members on "how health care was coming along."

"How's health care coming folks? We moving along? I think it's time now, right, they know it's time," Mr. Trump said.