Senate Majority Leader Mitch McConnell said Friday afternoon that Senate Republicans have enough votes secured for the GOP tax overhaul.

"We have the votes," the Kentucky Republican told reporters as he walked onto the Senate floor after huddling behind closed doors with the rest of the conference.

Senate Majority Whip John Cornyn said earlier in the morning that Senate Republicans had the votes to pass the sweeping GOP-sponsored tax overhaul measure.

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"We're confident in the 50 and we'd like to build on that," the Texas Republican told reporters.

By Friday afternoon, Sen. Bob Corker, R-Tennessee, was the only Republican on record who says he cannot vote for the bill, due to fiscal concerns.

"This is yet another tough vote. I am disappointed. I wanted to get to yes," Corker said. "But at the end of the day, I am not able to cast aside my fiscal concerns and vote for legislation that I believe, based on the information I currently have, could deepen the debt burden on future generations."

Sen. Susan Collins, R-Maine, officially announced Friday afternoon she would support the bill, listing the number of amendments she wanted that will be included in the bill.

"I don't think there is a single American who thinks that our current tax code is fair, simple, or promotes economic growth," she said in a statement. "We need a tax system that will boost the economy, help the middle class, and encourage small businesses to grow and create jobs. If we stimulate the economy through tax reform, we can significantly increase federal revenues while boosting Americans' take-home pay."

Sen. Jeff Flake, R-Arizona, announced in a statement after the closed-door meeting that he will support final passage of the plan, partially because he said leadership made assurances about resolving the Deferred Action for Childhood Arrivals (DACA) program legislatively. He said he also achieved the goal of eliminating what he described as a $85 billion "expensing budget gimmick" in the bill.

"Having secured both of those objectives, I am pleased to announce I will vote in support the tax reform bill," he said.

Following debate, members may offer an unlimited number of amendments, which is a period known as "vote-a-rama." Senate Republican leadership hopes to have the final vote Friday, but no final passage vote has been scheduled yet. Republicans continue to negotiate with their members to shore up the votes to pass the bill.

The GOP tax plan experienced a delay after the so-called "trigger" championed by Sens. Bob Corker, R-Tennessee and Jeff Flake, R-Arizona, was found to have violated Senate budget rules.

As a result, Senate Republicans are working on more changes to the legislation. The trigger would have raised taxes if future revenues or economic growth failed to meet the projections. A substitute for the trigger would be a "stair step" corporate tax increases over a period of time after the initial cut which could prove to be hard for conservative Republicans to swallow.

A Joint Committee on Taxation report found that economic growth from the tax plan would offset $407 billion of the nearly $1.5 trillion cost, adding $1 trillion to the deficit over a 10-year period. Republicans had claimed the bill would pay for itself. Republican leaders rejected the JCT's findings with Sen. John Cornyn, R-Texas, describing the JCT's estimates as "completely wrong."

CBS News' John Nolen, Alan He and Catherine Reynolds contributed to this report.