Washington (CNN) While Democrats didn't land a deal on immigration, the recent agreement to reopen the government nonetheless laid the groundwork for a potential Senate floor debate.

"We're very pleased with how it worked out," Senate Minority Leader Chuck Schumer, a New York Democrat, said Tuesday about the short-lived government shutdown, which drew attention to the standoff over the expiring Deferred Action for Childhood Arrivals program . "When there is a Republican president, a Republican Senate, a Republican House that (is) quite recalcitrant against Dreamers, you are not going to get it all at once."

However, even if the Senate passes an immigration bill in the next few weeks, there is widespread concern among Democrats that Republicans who control the House of Representatives won't take up the measure, much less pass it, in the face of pressure from immigration hawks in the chamber.

Democratic leaders, however, think they still have some leverage that could sweeten a bill and make it more appetizing to House Republicans, who refused to vote on a comprehensive immigration reform bill passed by the Senate in 2013.

CNN reported that Schumer outlined a list of potential bargaining chips Monday to the Democratic caucus, attempting to assure nervous colleagues who felt there was no path forward for a bill after it left the Senate.

Boosting defense spending

To start with, Republicans are anxious to boost defense spending, which would require lifting budget caps that were put in place during the 2013 sequester. Democrats are demanding an equal amount of spending increases for domestic programs. Leaders in both parties are negotiating behind the scenes to come to an agreement, but Democrats think they could potentially preserve this issue as an item to attach to an immigration bill, which could force House Republicans to take it up.

While Republican leaders and the President have said they would refuse to add immigration legislation to government funding bills, some Democrats privately think GOP leaders will reverse course if it's the only way to get an immigration bill through the House. If they did, it could infuriate House GOP conservatives who don't want to have to vote against spending increases for the military that they support in order to vote against an immigration deal they abhor.

Senate Majority Whip John Cornyn, a Texas Republican, said Tuesday he doesn't think an immigration bill needs to be attached to something else. "I know there's a lot of skepticism around here and not much trust, but I do believe there is a bona fide, bipartisan concern about getting this done."

Disaster relief package

Another point of leverage, Democrats feel, is an $81 billion disaster aid package for parts of the country that were affected by severe weather and natural disasters last year like Hurricane Harvey in Texas and Hurricane Maria in Puerto Rico. If it were tied to an immigration agreement, it could put enormous pressure on Republicans, especially delegations from Texas, Louisiana, Florida and other states affected by the damage.

DACA deadline approaches

In terms of a DACA deal, Democrats are counting on the fact that many Republicans don't want to be blamed for DACA recipients being deported after the program expires in March, so they're planning to ramp up the pressure as the midterm elections approach, especially in races where Republicans face tough battles to keep their seats.

"We now must move forward in a bipartisan way if we're going to finish the task at hand," Schumer said Tuesday on the Senate floor. "On the budget, on health care, on disaster aid, on DACA."

Senate Majority Leader Mitch McConnell, a Kentucky Republican, mentioned some of these legislative issues when he spoke Tuesday about the end of the government shutdown.

"Serious negotiations can resume on key issues such as immigration and border security, disaster relief, health care and providing adequate levels of defense spending to support the new national defense strategy, just to name a few," he said on the Senate floor. "Because common sense and bipartisanship won out yesterday, we have a fresh start today."

Funding after February 8

The agreement to end the shutdown keeps the lights on only until February 8, meaning Congress will face another deadline to pass what's expected to be another short-term spending deal.

Democrats are listing other priorities they want to get done with upcoming spending legislation, such as increased funds to fight the opioid epidemic; funds for community health centers, which expired in September; and relief for major pension programs that are struggling, like the Central States Pension Fund.

"I think we have leverage on all of them. We got to get 60," said Sen. Claire McCaskill, a Missouri Democrat, when asked which items give Democrats the best chance to negotiate the next spending bill. Because the Senate requires 60 votes to advance a bill, Republicans will need at least some Democrats to help pass it.

"It's too early to prioritize or say which ones have the best chance right now," said Sen. Gary Peters, a Michigan Democrat. Asked if the list was too long, Peters said, "It shouldn't be."

"It's the list the American people need," he added.

Many, meanwhile, expressed frustration with legislating major issues through must-pass spending bills.

"Stop making every single thing that comes up the-end-all-be-all," said Sen. Patrick Leahy, a Vermont Democrat. "I could go down through a list of 1,000 things that will never be something that makes a headline or make a story. ... But the fact is the American people are suffering right now."