Both matches are at Wembley and England go into them topping the group by one point from Montenegro, who are Friday's visitors, and Ukraine, and three clear of Poland, who provide next Tuesday's opposition.
Hodgson, appointed just before last year's European Championship, is confident England will complete the task and avoid the doomsday scenario of failing to reach the finals - something that last happened under Graham Taylor 20 years ago.
"My life at the moment is these two games," Hodgson told reporters this week. "As for the doomsday scenarios put before me, I won't have to confront them because I believe, and am confident, in that belief that the team will do it.
"Of course I am nervous, any coach worthy of the name is nervous when the whistle goes.
"But I believe we have the players to complete the task. I am certain as I can be that we will achieve our aim."
England are the only unbeaten team in the group, and will look to preserve that record against Montenegro without left-back Ashley Cole, who will miss the match with a rib injury.
The 32-year-old, who has played 105 times for his country, is likely to be replaced by Everton's Leighton Baines but has not yet been ruled out of Tuesday's match against Poland.
Baines will win his 20th cap if, as expected, he lines up alongside Everton team mate Phil Jagielka with the back four completed by Chelsea's Gary Cahill and Tottenham's Kyle Walker.
Steven Gerrard, Frank Lampard and Jack Wilshere are expected to play in midfield with Liverpool's free-scoring Daniel Sturridge and the Manchester United pair of Danny Welbeck and Wayne Rooney up front.
Rooney, Sturridge and Welbeck all missed the sterile 0-0 draw with Ukraine in Kiev a month ago.
Joe Hart will keep his place in goal despite a recent loss of form.
Wilshere is confident England will qualify and he is delighted to be in the mix after publicly expressing his regret after being photographed smoking a cigarette outside a nightclub last week.
"I know what I did was wrong, it was a mistake and I have learnt from it and I have apologised," he told reporters on Tuesday.
Montenegro come to Wembley hampered by injuries to four players who are all likely to miss the match including captain Mirko Vucinic.
Goalkeeper Mladen Bozovic, centre-back Marko Basa and midfielder Miodrag Pekovic have all been ruled out while defender Miodrag Dzudovic is doubtful because he has a back injury as well as an injured hamstring.
Two years ago, in a Euro 2012 qualifier, Dzudovic was the player kicked by Rooney which led to the England striker's red card 17 minutes from the end of a 2-2 draw in Podgorica.
That match is one of three the two countries have played against each other and all three have ended all-square.
Dzudovic believes another draw against England at Wembley and a win in their last match against Moldova could be enough to see Montenegro guaranteed a playoff place.
"But we will go for a win against England because we can't just roll over and throw away all the good work we have done in the qualifiers so far," he said.
"With the right attitude and self-belief we can finish in the top two and reach the playoffs."