Arizona's eighth Congressional District was considered to be a safe seat for Republican Debbie Lesko till a few weeks ago.
However, the aggressive campaign by medical physician Tipirneni and a general growing anti-Republican mood across the country appears to have tipped the balance.
USA Today has described the situation as "nervous" for GOP.
A new Emerson College ePoll has Tipirneni in a statistical dead heat with Lesko 46 per cent to 45 per cent.
Trent Franks, the former congressman who resigned in the wake of allegations of sexual misconduct, has a 24 per cent favourable and 49 per cent unfavourable opinion. Trump's job approval in the district is 44 per cent approve and 46 per cent disapprove.
"Arizona's special election has captivated national attention, with Republican groups pouring more resources into the district that was won by Trump in 2016. Dr Hiral Tipirneni has an opportunity to flip a critical House seat from red to blue -- but only if all of us step up to support her before the April 24th special election," the Democratic Party said.