WASHINGTON (AP) — House Speaker John Boehner (BAY’-nur) says any immigration bill passing the House ought to have support from a majority of both Republicans and Democrats. That’s a high bar on a difficult, often partisan issue.

Speaking to reporters on Tuesday, Boehner criticized a bipartisan Senate immigration bill, saying it is weak on border security. Boehner spoke on the same day the House Judiciary Committee was taking up a tough enforcement-focused measure that Democrats and immigrant groups are protesting loudly.

Both the House and Senate are working to overhaul the nation’s immigration laws. Senate Democratic leaders hope to pass a bill by July 4. The House is moving more slowly.