Monk has overseen just one win in 10 games since replacing Michael Laudrup just over seven weeks ago.
Swansea go into Saturday's match just five points clear of the relegation places, but Taylor is adamant Monk is the man for the long term.
"We definitely think he is the right man to take us forward. We are all giving our all for him," Taylor said.
"You can talk about experience, but he has got experience from three or four of the best managers around at the moment - (Roberto) Martinez, (Brendan) Rodgers and (Paulo) Sousa. He has learnt from all of them.
"He was captain under a lot of them, and he has been at the club for 10 years. He knows this football club better than anyone."
Victory over Liberty Stadium visitors Norwich would give Swansea much-needed breathing space, and Taylor knows that points are all that matter at this stage of the season.
"It wasn't pretty against Arsenal, it wasn't really the Swansea way the other night, but we scrapped and gave it our all. We got a good point, and maybe could have got three," he added.
"It will take our quality that we have on the ball and that bit of scrapping. If we can do both, we will be more than a match for all these teams around us.
"It is a must-win game. You have got to go out and do it now. It is going to go right to the wire at both ends of the table this year.
"When things are going great, like they were last season, things flow and everyone is happy, but this is the sticky end of football and you have got to show a bit of character.
"We've got to be right on top of each other as players and push each other right to the end of the season. It is time for everyone to be ready and to perform."