The Dow Jones Industrial Average slipped 0.5 percent shortly after trading started, to 32,741.25.

The broad-based S&P 500 ticked down less than 0.1 percent to 4,178.09, while the tech-heavy Nasdaq Composite Index was nearly flat at 12,934.34.

The debt limit deal is anticipated to clear the Senate after getting the green light from the House of Representatives, likely heading for President Joe Biden's approval before the country runs out of funds to pay all its obligations.

But market movements were muted following a rally last Friday and expectations that the deal would be done before the deadline, said Patrick O'Hare of Briefing.com.

There is also "a narrative at work that the market could now run into a wall of liquidity constraint as the Treasury Department replenishes its general account," he said.

Hammered out between Biden and Republican leaders, the pact suspends the debt ceiling through 2024, slightly cutting government spending next year.

The market was bought up before on the rumor of the deal getting done, said Adam Sarhan of 50 Park Investments.

With the deal likely to clear subsequent hurdles, "there's a high likelihood that the market drops a little bit to digest and move before going higher again," he said.

On Thursday, payroll firm ADP also reported that private sector job gains slowed less than expected, indicating continued strength in the key labor market.

Among individual companies, shares of software company Salesforce slumped 6.1 percent and artificial intelligence firm C3.ai plunged 22.4 percent, both after reporting their latest earnings.

Meanwhile, luxury department store chain Nordstrom's shares rose 7.2 percent.