Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.) told reporters Wednesday that he has spoken to President-elect Donald Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE about moving ahead with a repeal of ObamaCare as soon as possible.

McConnell said repealing the controversial healthcare law has strong support among Republicans on Capitol Hill, noting that not a single Republican voted for it in 2009 when it passed the Senate.

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“It’s pretty high on our agenda, as you know,” McConnell told reporters at a Wednesday press conference. “I would be shocked if we didn’t move forward and keep our commitment to the American people.”

He declined, however, to say whether Senate Republicans would use a special process known as budgetary reconciliation to kill the law on a straight party-line vote.

One of his deputies, National Republican Senatorial Committee Chairman Roger Wicker Roger Frederick WickerBottom line Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' MORE (Miss.), told reporters earlier in the day that he hoped the special budgetary process might not be necessary and that Democrats might be willing to negotiate reforms.

“Let’s see if we can reach some sort of consensus with our Democrat friends to make this repeal and replace [work],” Wicker told reporters. “I would hope that members of the Democratic Party are looking at the election results … and also not only that but the premium increases and would understand that the American people are dissatisfied with this failed program.”

Republicans have used reconciliation previously to get around the Senate's filibuster and approve ObamaCare reform.

McConnell also said overhauling the tax code and ramping up security along the U.S.-Mexico border are top priorities for the new Congress.