(CNN) Several high-profile Republican senators cast doubt Thursday on the chances of the GOP leadership plan to replace Obamacare, saying the process is moving too quickly and adding to a raft of woes for House Speaker Paul Ryan and President Donald Trump.
"The House bill as currently drafted, I don't believe will pass the Senate," said Sen. Ted Cruz, one day after he and his family dined with Trump and first lady Melania Trump as part of the President's efforts to woo conservatives to support the plan. However, the Texas Republican added: "We can fix it."
Since Republicans can't count on any Democratic support to get through Congress, GOP leaders are counting on a near-uniform front to advance the health care legislation, a level of unity that wasn't on display over the past several days in either the House or the Senate.
House leaders are also trying to advance this leg of the Obamacare repeal as part of the reconciliation process, which helps inoculate the bill from the threat of a filibuster but means leaders wanted the legislation wrapped in advance of the mid-April Easter recess. That deadline, however, did not appear to work for Sen. Tom Cotton.
"No normal American cares whether a health care bill passes before the Easter recess or the Memorial Day recess or any other recess," the Arkansas Republican told reporters. "They don't care that we get health care done fast. They care that we get it done right."
Cotton, generally seen as a Trump ally, blasted the House Thursday morning, accusing them of ramming health care through the same way that Democrats did eight years ago.
"House health-care bill can't pass Senate w/o major changes. To my friends in House: pause, start over. Get it right, don't get it fast," Cotton tweeted Thursday morning.
Cotton added: "What matters in long run is better, more affordable health care for Americans, NOT House leaders' arbitrary legislative calendar."
Conservatives in the House have laid out a set of demands they say is needed to earn enough votes for the bill to pass the chamber. And even as House lawmakers worked through the night Wednesday and into the morning Thursday pushing through the health care bill, the White House and House Republican leaders continued their coordinated lobbying effort.
And other senators have said they simply don't want to weigh in without seeing the impact the Congressional Budget Office determines in its "score" of the proposal.
"It's kind of crazy they're voting without a score," Sen. Bill Cassidy, a Louisiana Republican, said Thursday.
Cotton also raised those concerns in a tweet.
"GOP shouldn't act like Dems did in O'care. No excuse to release bill Mon night, start voting Wed. With no budget estimate," he continued.
And members of the House felt the pressure of the leadership's timeline. Asked about Cotton's tweets, Rep. Steve King agreed that House Republicans were moving too quickly and did not give Congress enough time to improve it.
"We should have had more time to digest it. I would have rather seen it out for a week or 10 days before they go to a committee and mark it up," the Iowa Republican told Cuomo. "It really isn't much time for anybody to bring amendments to try to make the change."
Republicans can only afford to lose a few votes in the Senate, and some members have been vocal with their criticism including Sen. Rand Paul, who's repeatedly called the current bill "Obamacare Lite."
But Senate GOP leaders insist they will have enough support to pass health care through the Senate.
"We don't know what the House bill is yet, because it hasn't passed the House," said Senate Majority Whip John Cornyn. "We have been working very closely with them because we want to make sure that whatever they send us passes the Byrd Rule Test."
"We will pass it and it will be signed by the President," Cornyn said.