The hosts enjoyed another day of dominance in Southampton on Tuesday, restricting India to 323-8 in response to their first-innings total of 569-7 declared.
Seamers Broad (3-65) and James Anderson (3-52) were the star men in the England attack, while spinner Moeen Ali contributed with 2-62 as India finished the day 246 runs behind and needing another 47 to avoid the follow-on.
India captain MS Dhoni is still at the crease on 50 not out, and Broad believes an aggressive mentality will be key for England in their quest to knock off the tourists' lower order.
"It's going to be an important hour for us tomorrow morning to get those two wickets," he told the England and Wales Cricket Board's official website.
"Dhoni can be hugely dangerous when he bats with the tail, so we need to come out with the same energy we had today.
"It's been a fantastic day for us I think. At the end of day four, day five, it [the pitch] will deteriorate nicely.
"To have got ourselves in a position like we have done is credit to the whole bowling unit - regardless of who picked up wickets, we created pressure the five of us that bowled and I think it's a rewarding day for the hard work we've put in."
However, Broad conceded that he and the other members of the England attack are in need of some respite and revealed that he would not enforce the follow-on if he were captain as the hosts aim to win their first Test match since last August.
"I'd bat again, get 400 ahead, give the bowlers a bit of rest and get back in the field," he added.
"We worked hard as a unit all day and we deserved a bit of luck towards the end.
"We've played some really good cricket in this Test match and we're due a win - and every player in that dressing room is desperate for that."