The Senate majority leader can afford to have only two of his members side with the Democrats if the minority leader forces a chamber vote on whether to allow witnesses during the trial.
The Senate is expected to pass the short-term funding bill, known as a continuing resolution, but President Donald Trump still has to sign it.
The chances that McConnell may soon have to face that reality have become increasingly likely, as House Democrats are surging forward with their newly launched impeachment proceedings amid news that Trump pressured a foreign leader to investigate a political foe.
Trump has no shortage of opponents, but here are some Republicans who have made their opposition known.
If Democrats hope to succeed in their plan someday becoming law, they must navigate the criticism and address the concerns levied by Republicans, Trump and even some of their own members about how to address raising drug prices.
GOP members indicated that, while they may support certain gun violence prevention measures, they're unwilling to take action without support from Trump because efforts would be futile to only be defeated by a presidential veto.
Senate Republicans "are reprehensible in what they're doing. Their families have to understand what traitors they are to their conference, to their party and to the country," Lou Dobbs said.
The White House "is trying to use tariffs to solve every problem but HIV and climate change," one Republican senator said after Tuesday's meeting with White House officials.
"I don't think it's designed to get Democratic support as much as it is to unify the Republican Party around border security," Republican Senator Lindsey Graham told reporters Tuesday.
The Republican senator's Intelligence Committee members did not seem very enthusiastic about hauling the president's eldest son before the committee for a second round of questioning.
"At this rate, McConnell and Trump could leave few, if any, vacancies open in 2021," the Democratic Senatorial Campaign Committee said.
At the White House earlier, the president would not commit to supporting or vetoing the bipartisan measure.
The resignation of Cochran Monday complicates Republican plans to hold on to the Senate.
The chorus of GOP Senators speaking out against Trump exposes deep divides ahead of the 2018 midterms.
Senator Corker called President Trump harmful and said he is "absolutely not" a role model for the country.
The plan has passed the Senate and is likely to get through the House next week.
Liberal groups seize on the Senate health care vote delay to intensify opposition, while conservatives do outreach behind the scenes.
Citing time crunch, Democratic opposition, Republicans are weighing major policies and nominees without the usual oversight.
Senate GOP leaders prefer to work with Vice President Mike Pence.
Without public buy-in or bipartisan support, any measure Republicans pass is likely to be temporary.
Russia investigations, a lack of federal and Republican support and repeated leaks mean the president looks less and less in control.
Facebook says it found no evidence that the company excluded conservative news outlets from its trending feed.