Senate Majority Leader Mitch McConnell of Ky., left, and Senate Majority Whip Sen. John Cornyn, R-Texas depart after speaking with the media after they and other Senate Republicans had a meeting with President Donald Trump at the White House, Tuesday, June 27, 2017, in Washington. (Alex Brandon/Associated Press)

WASHINGTON — The Latest on the Republican legislation overhauling the Obama health care law (all times EDT):

5:55 p.m.

Senate Majority Leader Mitch McConnell says “good progress” was made during a White House meeting between President Donald Trump and Republican senators.

Trump invited them to meet after McConnell decided to delay a vote on a Senate health care bill because there aren’t enough votes to pass it.

McConnell said after the meeting there’s a “really good chance” of passing the bill, but it won’t happen before July Fourth as he originally planned.

McConnell says Republicans must come up with a solution because that’s why the American people elected them. He says negotiating with Senate Democrats won’t produce any of the changes sought by Republicans, including to the health markets and Medicaid.

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4:35 p.m.

President Donald Trump says that if the health care bill fails to pass in the Senate, he won’t like it — but “that’s OK.”

Trump spoke Tuesday at a gathering of Senate Republicans after their leaders shelved a vote on their prized health care bill until at least next month.

Trump says, “This will be great if we get it done and if we don’t get it done it’s going to be something that we’re not going to like and that’s OK and I can understand that.”

He adds, “I think we have a chance to do something very, very important for the public, very, very important for the people of our country.”

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4:30 p.m.

Add three more names to the list of Republican senators saying they oppose the GOP health care bill.

But these three get an asterisk. They released statements of flat-out opposition after Senate Majority Leader Mitch McConnell said he was delaying the vote in hopes of rounding up enough support for passage.

Sens. Rob Portman of Ohio and Shelley Moore Capito of West Virginia have persistently criticized the bill’s cuts in Medicaid, and have sought billions more to combat opioid abuse. Both said for the first time Tuesday they opposed the measure.

Sen. Jerry Moran of Kansas said last week he would examine whether the proposal was good for his state. He said Tuesday the bill did not have his support, saying he wanted more affordable and better quality health care.

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4:25 p.m.

President Donald Trump says he wants the replacement of the 2009 health insurance law to increase the number of insurance coverage choices and lower premiums, a senior White House official says.

The president was stressing these goals in a meeting Tuesday with Kentucky Sen. Rand Paul, a Republican who opposes the Senate’s planned replacement of the government’s health insurance expansion under former President Barack Obama. The official insisted on anonymity to describe private conversations.

Senate Majority Leader Mitch McConnell of Kentucky has delayed a vote on that replacement, which has been unable to attract sufficient support from Republican lawmakers. The replacement would reduce funding for Medicaid, cut taxes on investments and cause 22 million fewer people to no longer have health insurance, according to the Congressional Budget Office.

— Josh Boak

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4:20 p.m.

President Donald Trump and Vice President Mike Pence are hosting Republican senators at the White House to discuss flailing efforts to pass a new health care bill.

Most of the GOP senators arrived at the White House Tuesday after Senate Republican leaders shelved a vote on their prized health care bill Tuesday until at least next month.

A GOP rebellion left them lacking enough votes to even begin debate.

Trump said Tuesday that “we’re getting very close but for the country we have to have health care.”

Trump invited the GOP senators for a meeting in the East Room to discuss efforts to repeal and replace former President Barack Obama’s signature health care bill.

He says “I think the Senate bill is going to be great.”

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2:40 p.m.

Senate Majority Leader Mitch McConnell says he is delaying a vote on a Senate health care bill while GOP leadership works toward getting enough votes.

He says they are “still working toward getting at least 50 people in a comfortable place.”

Republican senators are headed to the White House Tuesday afternoon to talk to President Donald Trump about the future of the bill.

McConnell says the White House is “very anxious to help” and encouraged senators to go to the meeting.

McConnell said health care…