Senate Democrats have said the first amendment considered would come from Sens. Joe Manchin (D-W.Va.) and Pat Toomey (R-Pa.), which would dramatically scale back the extent of new background checks under the bill. Their amendment would only expand background checks to online gun sales and sales at gun shows, and would also prohibit a national firearms registry.
As the Senate wrestles with gun control, the Senate's bipartisan Gang of Eight is expected to unveil an immigration reform proposal that promises to be about as controversial as the gun issue.
The plan will call for the creation of a path to U.S. citizenship for millions of people now living in the U.S. in violation of the law, and some measure of increased border security.
But for many Republicans, tougher border security is a required first step before there can be any talk about pathways to citizenship. A few House Republicans said they spent some time on the southern U.S. border during the Easter break, and said their assessment is that the border is not secure, despite claims to the contrary from the Obama administration.
Next week is also "cyber week," as the House will take action on a handful of cybersecurity bills. One of them is a bipartisan bill that would let the government share classified information about cyberattacks and protect companies from liability for sharing similar information.
Last year, the White House said it would veto the same bill, but this year, the administration stopped short of that threat, and said it hopes to work with Congress on this bill.
Other cyber bills up this week would boost cybersecurity research and update the government's cybersecurity framework.
Off the floor, the Senate Judiciary Committee will hold a hearing Wednesday on immigration, a day after the bipartisan immigration proposal is due to come out. In the House, committees will hold several oversight hearings, including one that examines how the administration has prioritized sequester cuts at the Transportation Security Administration.
Below is a more detailed look at the week ahead:
The House meets at noon, and will work on suspension bills throughout the day, with a roll-call vote expected by 6:30 p.m. The suspension bills are:
H.R. 1162, the GAO Improvement Act,
H.R. 249, the Federal Employee Tax Accountability Act,
H.R. 882, the Contracting and Tax Accountability Act, and
H.R. 1246, the District of Columbia CFO Vacancy Act.
The Senate meets at 2 p.m., and will likely continue debate on the gun bill, S. 649, the Safe Communities, Safe Schools Act. But the first vote of the week will be at 5:30 p.m., when senators consider the nomination of Beverly O'Connell to be a district judge for the central district California.
The House starts work at noon on three cybersecurity bills. All three are suspension bills, which will require a two-thirds vote for passage. They are:
H.R. 1163, the Federal Information Security Amendments Act, to update federal cybersecurity systems,
H.R. 756, the Cybersecurity Enhancement Act, to increase cybersecurity research, and
H.R. 967, the Advancing America's Networking and Information Technology Research and Development Act, to aid information technology research.
The Senate is in for the rest of the week, and Democrats are hoping to begin consideration of various amendments to the gun bill.
The House will consider H.R. 624, the Cyber Intelligence Sharing and Protection Act, under a rule. This is the bill that attempts to make it easier for the government and companies to share information about cyberattacks, in the hopes of stopping them. The House will likely pass the rule for this bill Wednesday, and then pass the bill on Thursday.
The House is out.