The House has a few exclusive powers that the Senate does not. The House is the only one of the two that can initiate money bills. The president himself nor EXOP can do such a thing. This offers the House of Representatives a large scope of power in financial issues abroad and domestically. Impeachment is also another power possessed by the House. If a president or a member of the federal government has been acting illegally or unconstitutionally the House can impeach - formally accuse - them of it. This is then trialed in the Senate, but offers the House a lot of power over the president, and helps congress with it's scrutiny of the executive.
The Senate also has a few exclusive powers that are strong in the right circumstances. The senate confirms appointments by a simple majority to most appointments made by the president. These include all the president's appointments to the federal judiciary and most of the appointments to the executive branch. This results in the president needing the senate's consent a lot of the time. The second significant exclusive power is the power to ratify all treaties negotiated by the president, by a two-thirds majority. This means that the president needs to keep the Senate fully informed throughout treaty negotiations, to avoid concluding treaties that the Senate is unlikely to ratify. After the House has impeached someone, the senate is also responsible to try that case of impeachment. Recently the House tried to impeach President Clinton, but it was acquitted by the Senate in 1999. These powers show control and restrictions on the president and offer congress power in domestic issues and foreign.
The president of the United States of America is seen as the most powerful man on Earth by almost all foreign countries. This is because they see his foreign power, and not his lack of domestic power. The way the relationship between the legislature and the executive in the United States of America works, is that the executive deals with most of the foreign policy, and the legislature most of the domestic. For example, the president is the one who negotiates treaties, who attends all of the peace talks, united nations summits and so forth. Though he does need to get a two-thirds majority to ratify any treaties, and a majority to declare war, the president has other powers in foreign policy. For example, a president is commander-in-chief. He is leader of all the armed forces. The only constitutional power congress has in this respect is to declare war, which hasn't been used since 1941. Other than that congress has no power over the use of troops. However, a president now asks congress to authorise his use of troops, though this is not constitutional, and therefore not necessary. The president's dominance in foreign policy leaves congress with very few powers in that area but the Senate's two thirds majority for the confirmation of treaties.
However, in Domestic policy the president is a lot less important, and this is where congress comes in. The president and even EXOP do not have time nor the resources to make laws like the committee's of congress do. Instead EXOP merely advises the president on what bills to support, and what not to, if indeed he needs advice. The only power the president has over congress in this area is his veto, but this can be countered with a two thirds majority in both houses. If both houses had a two thirds majority of the party opposing the president and there was never any swing it would be purely congress's law. However, this doesn't happen in practice, but it could. The president has little input and power over domestic issues and law, and congress dominates it. However, the president has a lot more power than congress in foreign affairs.
To truly analyze the strength of congress, we must look at the variables. The key ones being: the party's of the executive and both houses of congress, their sizes and their leading figures. Firstly if there is a particularly strong congress, and a weak president, then congress will be very dominant. If for example, like the late Clinton (Democrat), you are facing a Republican Congress, then you have relatively little power domestically. If the republicans had two thirds in each house, it would render the president powerless in the passage of law, as even if he veto'd, he could be over ridden. Also, he could be a bit more restrained in foreign policy without such a majority. If the republicans have the senate, then without a large swing vote, it is impossible for the president to get his treaties passed, so it would have to be a lot of what congress want in there too to get the two-thirds support it needs to make it into law.
However, on the opposite end of the spectrum there are presidents like Reagan who was a strong president versus a weak congress. He often got over two thirds of the vote in each house. He used various methods like well written speeches, or phone calls to individual congressman to persuade them to help him out. His party also had control of both houses, which made things a lot easier for him. This is where congress begins to lose it's power of scrutiny, because it's not so much a check of the executive, but a rubber stamp for it's decisions, especially with a very persuasive president such as Reagan.
Although these events of an extremely weak congress and a powerful president and vice versa are possible, they are not regular, and the power of both the executive and the legislature depend on a two way relationship. Often neither party will be in presidency and have both houses, and they will rarely have a house by more than a two thirds majority. This makes the relationship between the presidency and congress a very important one. Both rely on the strength of one another, as no one has the power to be dominant. A president needs a lot of support for his foreign treaty's for example, which he wont be able to muster even if he gets all of his party's support. The same with congress, if the president veto's legislation, then they would not have the unity if there was no swing to over power him. This means that both sides have the power to deadlock the system, so it is incredibly important that they maintain this relationship.
A lot of the time it is a simple trade of legislation, or the addition of something that both sides can agree on. Or it can be a simple persuasion, a president can try and go against the will of the opposition majority party in congress by persuading a lot of it's members to vote for his bill, and get it passed. Most presidents don't have this sort of power, and even if they do, congressman expect something in return, often for him not to veto their legislation, and either sign it or leave it on their desk.
In conclusion, the power and significance of congress is variable under circumstances, but it is typically great in domestic issues, and fairly weak in foreign ones. It's significance is always great in the law making process, however variable it is elsewhere.
