The administration-hit Tynecastle outfit were handed a 15-point punishment at the start of the season for breaching insolvency rules and were immediately installed as the 8/13 favourites to finish bottom of the Scottish Premiership.
But two wins and a draw from their first five games has seen Hearts reduce the gap separating them from second-bottom St Mirren to just nine points.
Now with champions Celtic to come on Saturday lunchtime, Walker insists their pre-season critics have only made the team more determined to go on and complete a remarkable escape.
He said: "It was a massive inspiration for us. Everyone was against us, the odds in the bookies were against us. Everyone thought we were going to go down.
"But we've had a good start. We had some hard games but we've done well and everyone is buzzing ahead of Saturday.
"Now we want to prove the people who doubted us wrong.
"There is still a massive gap to St Mirren and we know it is going to be hard but we believe we have the quality to do it. We would take 11th place and a shot at the play-offs now but the start we have had has been amazing and now we are looking to go as high as we can."
However, Walker admits that Gary Locke's men will not be able to do it on their own.
"We've taken six points off St Mirren already at the bottom and hopefully over the coming weeks we can pick up a few more points while other results go our way too," he said.
"Because we are in this position, we will need results to go for us. But first and foremost, we have to do what we need to do on the pitch before we can hope for favours."
The Tynecastle encounter will be Celtic's last domestic test before they face AC Milan in the San Siro in their opening Champions League tie.
But Walker believes the boisterous Gorgie crowd can inspire the side to another victory after backing their team in opening home wins over Hibernian and Aberdeen,
He said: "Saturday will be our biggest challenge of the season. But at home we will fancy our chances against anyone, especially with the type of crowds we have had this season behind us again.
"It doesn't get any better than playing in front of a massive crowd at Tynecastle with the fans so close to the pitch creating a good atmosphere.
"We're unbeaten at home and we'll be looking to continue that."
Meanwhile, Hearts boss Gary Locke will be able to call on Jamie Hamill for Saturday's lunchtime fixture with Celtic after his Inverness dismissal was overturned.
The midfielder was shown a red card by referee John Beaton at the Caledonian Stadium for deliberate handball, but the Tynecastle club were successful with an appeal against the decision after TV pictures clearly showed the ball hit Hamill's face. Defenders Danny Wilson and Kevin McHattie are also available after serving a one-match bans against Caley Thistle.
The only Jambos player missing for the Scottish Premiership clash with last season's champions is Ryan Stevenson, who remains sidelined with a knee injury for another four weeks at least.
Provisional Squad: MacDonald, Hamill, McGowan, Wilson, McHattie, Robinson, Paterson, Walker, Holt, McKay, Smith, Carrick, B King, Tapping, Ridgers, A King, Nicholson, Oliver, McGhee, Combe.