WASHINGTON — Despite a broad budget deal, the White House and congressional Republicans must resolve dozens of policy issues and spending fights if they are to avoid a holiday season government shutdown.

Hot-button battles over Planned Parenthood, the environment and money for agencies like the IRS could still derail a must-do spending bill to keep the government running.

The goodwill that emerged from the bipartisan budget-and-debt bill that President Barack Obama signed into law on Monday could be short-lived as GOP leaders look first to sooth the feelings of rank-and-file Republicans opposed to the underlying budget pact. GOP leaders like Speaker Paul Ryan appear to be under pressure to show some fight and avoid getting steamrolled by Democrats and Obama, who bring plenty of leverage to the talks.

Filling in the details of $66 billion in additional spending for the Pentagon and domestic agencies — and sorting out dozens of policy battles — give a divided, dysfunctional Congress plenty of chances to stumble.

At issue is a $1.1 trillion-plus catchall bill to ensure the government stays open. Spending amounts are relatively easy to sort out, helped in great measure by the extra billions of dollars.

However, Republicans who control both the House and Senate are sure to try to squeeze agencies like the IRS and the Environmental Protection Agency, while Democrats will defend domestic departments and press priorities such as infrastructure grants, preschool education and money for local police and other first responders.

And then there’s Planned Parenthood. Tea party Republicans are insistent on stripping the organization of its federal funds because of its practice of collecting and distributing fetal tissue for scientific research. Former House Speaker John Boehner’s refusal to risk a government shutdown over Planned Parenthood money was the precipitating factor in his being forced out last month.

Also troublesome are dozens of GOP policy provisions that seek to reverse a slew of regulations issued by the Obama administration, including limitations on carbon pollution from coal-fired power plants, new clean water rules and financial restrictions from the Consumer Financial Protection Bureau established in the 2010 overhaul. Also in the cross-hairs is a Labor Department rule that would require brokers giving advice on retirement accounts to act in their clients’ best interests.

“The power of the purse rests within the legislative branch and we fully expect that we’re going to exercise that power,” Ryan, R-Wis., told reporters Tuesday at a news conference.