(CNN)Senate Majority Leader Chuck Schumer aims to put President Joe Biden's $1.75 trillion social safety net spending plan on the Senate floor by mid-November, setting up a potential clash with his most important swing vote, Joe Manchin, who has raised serious concerns about the proposal and called on Congress not to rush the process.

       "We hope the House to pass it soon and hope to begin debate on it on the 15th," Schumer said Tuesday, referring to the proposal to expand health care access, address the climate crisis, provide aid to families and deliver on other key liberal priorities.

       The timeline outlined by Schumer comes as top Democrats are racing to try to finalize a deal on the package and pass it out of the House as soon as this week. But Manchin, whose vote is critical to Senate passage, has continued to dig in over opposition to key elements of the plan and told CNN on Tuesday that he thinks it could take "a while" to finalize and enact the package.

       On timing, Manchin told CNN on Tuesday, "I just think it's going to take quite a while," reiterating his longstanding call for Democrats not to rush the process.

       "You're talking about overhauling the entire tax code. That is tremendous. And there needs to be input," he said. "We're not in a rush right now."

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       This story is breaking and will be updated.

       CNN's Morgan Rimmer contributed to this report.