The party, which rules India through a minority coalition, lost three of four key state polls held since last month, according to results unveiled on Sunday, in a major setback ahead of general elections due by May.
Although Finance Minister P. Chidambaram has repeatedly pledged the country will meet its fiscal deficit target of 4.8 percent of gross domestic product for the year ending in March, investors now fear the government could crank up spending in a bid to boost its electoral standing.
Fitch said on Tuesday the likelihood of that happening was increasing, but said the government has little room to manoeuvre on spending, given that India's fiscal deficit has already reached 84 percent of its target in the first seven months of the year.
"An evident anti-incumbency trend against the Congress could mean an increasing likelihood of political pressure to limit expenditure cut-backs," Fitch said in its note.
"This would help support economic recovery in the run-up to the national elections which must be held by May 2014. But it may raise some doubt about the government's ability to meet its stated near-term fiscal goals."
Fitch noted that unless revenue unexpectedly surged, India would ultimately need to cut spending if it wanted to meet its fiscal deficit target.
Investors are increasingly betting the Hindu nationalist Bharatiya Janata Party and its prime minister candidate Narendra Modi could win general elections next year after its strong showing in state elections.
Although Indian shares hit a record high on Monday after the state results because of widespread perceptions of the BJP as a more business-friendly party, bonds have struggled, partly due to fear of less spending restraint by the government.
The new benchmark 10-year bond yield is up 2 basis points at 8.87 percent this week.
Still, analysts said markets were willing to give the government the benefit of the doubt for now.
"The growth in the planned expenditure gives a lot of scope to cut back. So we have to give benefit of doubt to the finance minister," said A. Prasanna, an economist at ICICI Securities Primary Dealership Ltd.
Fitch returned India's outlook to "stable" in June, a year after it had downgraded it to "negative", citing the government's efforts to contain the fiscal deficit and revive economic growth.