US President Donald Trump attends a meeting with US House Deputy Whip team at the East room of the White House in Washington, US March 7, 2017. [Photo/Agencies]

"We're going to do something that's great and I'm proud to support the replacement plan released by the House of Representatives," Trump declared at the White House as he met Tuesday with the House GOP vote-counting team. "We're going to take action. There's going to be no slowing down. There's going to be no waiting and no more excuses by anybody."Meanwhile, Vice President Mike Pence told GOP lawmakers at the Capitol this was their chance to scuttle Obama's law, and Senate Majority Leader Mitch McConnell forecast congressional passage by early April.

But major obstacles loomed as key Republican lawmakers announced their opposition, and one conservative group after another torched the plan. The Club for Growth, Heritage Action for America, Americans for Prosperity and Tea Party Patriots variously derided the new bill as Obamacare Lite, Obamacare 2.0 and even RyanCare, in a dig at House Speaker Paul Ryan of Wisconsin.

The new GOP plan would repeal the current law's unpopular fines on people who don't carry health insurance. It also would replace income-based subsidies, which the law provides to help millions of Americans pay premiums, with age-based tax credits that may be skimpier for people with low incomes. Those payments would phase out for higher-earning people.

The legislation also would limit future federal funding for Medicaid, which covers low-income people, about 1 in 5 Americans. And it would loosen rules that Obama's law imposed for health plans directly purchased by individuals.

Republican supporters and opponents are all intent on reducing the role of government in health care, but some House conservatives say the new bill doesn't go nearly far enough.

For example, they are focusing on the system of refundable tax credits they denounce as a costly new entitlement. They're demanding a vote on a straightforward repeal-only bill.

At the White House meeting Tuesday, Trump made clear to House Republicans that he would be personally engaging with individual members who oppose the bill as leadership tries to round up votes, according to a lawmaker present who spoke on condition of anonymity to discuss the private gathering.

Not long after, Trump appeared to be making good on his promise, tweeting at Sen. Rand Paul of Kentucky, who has criticized the bill.

"I feel sure that my friend @RandPaul will come along with the new and great health care program because he knows Obamacare is a disaster!" the president wrote.