Sen. John Cornyn John CornynHillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close Lawmakers introduce legislation to boost cybersecurity of local governments, small businesses On The Trail: Making sense of this week's polling tsunami MORE (Texas), the Senate's No. 2 Republican, says a key vote to advance the GOP ObamaCare repeal bill will likely occur on Wednesday.

"It's looking a little more like tomorrow right now," Cornyn told reporters on Tuesday, saying a formal announcement could come later in the day.

Leaders currently do not have the support to win that procedural vote, known as a motion to proceed, to take up the bill for consideration.

At least four GOP senators — centrists Susan Collins (Maine) and Dean Heller (Nev.) and conservatives Rand Paul (Ky.) and Ron Johnson (Wis.) — say they may vote against their party on the motion to proceed, underscoring the opposition to McConnell’s bill.

McConnell can only afford two defections, assuming Vice President Pence breaks a 50-50 tie, and a loss on the procedural vote would certainly end work on the measure this week.

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Asked if leaders would call a vote even without the support to advance the bill, Cornyn instead pledged leaders would prevail.

"I'm not willing to accept the hypothetical. We're going to vote and we're going to pass it," he said.

He reiterated that the vote would not be delayed past this week. Leaders are pushing forward to move the bill before the July 4 recess, despite resistance from both conservative and moderate wings of their party.

There are "continuous conversations" about changes to the bill, Cornyn said, but none have been finalized yet.

One possible change is to add more money for opioid treatment in an effort to bring on board more moderate lawmakers.

"That's an item of discussion," Cornyn said Tuesday.

Lobbyists also said there has been discussion of easing the rules to allow for expanded health savings accounts, something favored by conservatives.

But conservatives such as Sens. Mike Lee Michael (Mike) Shumway LeeBipartisan representatives demand answers on expired surveillance programs McConnell shores up GOP support for coronavirus package McConnell tries to unify GOP MORE (R-Utah) and Rand Paul Randal (Rand) Howard PaulRon Paul hospitalized in Texas The Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Rand Paul says he can't judge 'guilt or innocence' in Breonna Taylor case MORE (R-Ky.) are pushing for significantly larger changes than that, such as regulations on pre-existing conditions.