Republicans control Congress but cannot keep the government running without Democrats, and several Democrats have said they will not vote for a spending bill unless it also resolves the plight of the immigrants. “We will not leave here without a DACA fix,” Representative Nancy Pelosi, the House Democratic leader, said on Thursday.

The multipronged campaign to help the young immigrants underscores how much the country has come to identify with them and how extensively they have been integrated into the economy. Many Republicans have joined Democrats in supporting DACA beneficiaries, and polls show overwhelming support for them. It is no longer politically risky to get behind them.

At the same time, many of the ads, videos and demonstrations are sidestepping the major sticking point, an issue that has divided some immigrant groups themselves. Leading Republicans have said any relief for the young immigrants must be paired with bolstered border security, more restrictions on legal immigration, or both, a trade-off that is usually left unmentioned in the advocacy.

In a recent conference call with religious leaders who supported helping the immigrants, one Republican, Representative Peter Roskam of Illinois, told them he would support legislation to shield the immigrants from deportation only if it came with enhanced border measures. In a statement on Wednesday, Mr. Roskam’s office said his view had not changed.

The mobilization began in September, as soon as the Trump administration announced the repeal of the deferred-action program.

The following month, some 60 businesses, trade associations and other groups representing virtually every major industry formed the Coalition for the American Dream. Among the participants are Coca-Cola, Western Union, Ikea, Hilton and Marriott.