If the President is incapacitated and his party has a narrow House majority and 50-50 Senate...

[President Johnson]

I don't understand the particular question. It is up to the vice president and the cabinet to invoke the 25th Amendment in case the president can't fulfill his duties. Congress only comes into play here when the president issues a written declaration objecting to the transfer of presidential authority. And in this case, a two-thirds majority is needed to keep the president out of power (that's also why the 25th was never a realistic option during the Trump years; it's just that nobody bothered to look up what the 25th says and apply political realities).

Or do you actually mean Section 2, that allows the president to fill a vice presidential vacancy by nomination of a new vice president? Either because the latter resigned/died or because he succeeded to the presidency. In this case, a nominee would definitely get confirmed, barring a major scandal surfacing during the confirmation process. Biden or Harris would definitely get a new vice president today, but I'm not so sure that would be the case with a Republican congress. Vise versa, a Democratic congress would probably still confirm a non-controversial Republican vice president. For example if Trump or (President) Pence nominated someone like Nikki Haley or Rob Portman in 2019, the Democratic House would have approved the nomination.